tl:dr: Starting from the 19th century it took until after 1945 to form "modern classic Italian cuisine". These beginnings curiously coincide with the widespread adoption of tomatoes for pasta dishes. As a sauce ingredient, tomatoes gained popularity earlier. Basil was only modestly popular compared to other herbs, but it was so indeed since it first came to Italy.
Italy only exists as a unified state since the middle of the 19th century. ("it is true that the problem of 'creating Italians' emerged after national unity had been achieved") The country is as the language starkly contrasted between North and South. And this is reflected in the kitchen systems. A 'national' cuisine did not came into being at first. Since the middle ages cookbooks with local or regional focus were written in Latin, then French and finally in vernacular Italian.
Keeping in mind that for upper classes 'Italian' cuisine was at the absolute forefront of culinary excellence in Europe, before a Medici bride entered the French court and initiated the advance of French cooking.
As such, the "Italian cuisine" or 'national cuisine' is late and deliberate construction, still not very well reflected in everyday life in Italy itself. Only at the regional level was the commonality of recipes observable to a greater extent. That would make a list of a few 'cuisines': mainly Liguria, Lombardy, Venice, Tuscany, Emilia and Romagna, Rome, Naples, and Sicily.
The History of the pizza would be one example: Until the beginning of the 20th century, pizza and pizzerias remain a purely Neapolitan phenomenon, and only gradually Italian.
A question for a quintessential Italian dish may be answered with 'pasta with tomato sauce'. But thinking of "then it must be slightly younger than the Columbian exchange" falls short of the actual integration of the fruit into that dish. It took until ~1820 that the olio and cheese variants had to share the spotlight with the tomato-dish. Although Neapolitan recipes generally still prefer another variant for pasta with meat.
From this cerebral construct of 'national identity' as difference we observers note the following:
The “local” product, if consumed only at a local level, is devoid of geographical identity, since identity comes into play through a process of relocation, of “delocalization.” Mortadella from Bologna is called “Bologna” only when it leaves the city where it is produced. “Ascoli-style olives” (olive all’ascolana) assume this name when they travel beyond the borders of Ascoli, even if they are promptly shipped back there, bearing this name, in a kind of boomerang effect.
The 'typical Italian cuisine' and its history is now largely obscured through a century of marketing and re-branding via Italian immigrants, mainly to the US:
Italy’s culinary heritage is usually asserted and recognized through references to city-based identities. This is evident not only in the names of elaborate recipes and food preparations that were devised in urban settings, in the workshops of culinary artisans or, more recently, in industrial establishments (Cremona relish and Neapolitan spaghetti, for example) but also in the names of products originating in the countryside, the mountains, and the sea. When we speak of Treviso chicory, Bitonto oil, Ravenna turbot, Messina swordfish, Sorrento walnuts, or the ewe’s-milk cheese called pecorino romano, we are highlighting marketing centers rather than the areas where these foods are actually produced. It is understandable that the most successful “typical” products in the history of Italian food are those with the strongest industrial support (we have only to think of pasta, Parmesan cheese, and tomato sauce). These, in effect, are the products that travel best.
These late — and industrialised — additions to the culinary arsenal are so dominating the picture today that it seems complicated to unearth 'authentic' Italian recipes. Which of course, never existed in the first place, if we mean to understand 'never changing since the fall of Rome'.
Focusing back on the gift the Genoese brought back:
But unlike France, where Parisian cuisine competes with Provençal cooking, Italy, though gastronomically divided by regions, gains from its decentralized character and manages to sell pizza with tomatoes everywhere, popularized by emigrants of southern Italian origin.
The tomato, initially regarded as an ornamental fruit and later adopted as a food, was an exotic curiosity that first appears in the writings of P. A. Mattioli and José de Acosta, travellers and naturalists. Apart from these sources, allusions to its consumption are very rare. Costanzo Felici tells us, however, that the usual “gluttons and people greedy for new things” did not realize that they could eat the tomato as they would eat mushrooms or eggplants, fried in oil and flavored with salt and pepper. Although we must not exclude the possibility that tomatoes were consumed at an earlier date by the common people, it is only at the end of the seventeenth century that we observe their inclusion in elite cuisine, thanks to the Neapolitan recipe collection of Antonio Latini. Iberian influences may be detected in their adoption for culinary purposes, since various recipes that call for tomatoes are designated as “in the Spanish style.” Among these is a recipe for “tomato sauce,”41 which is flavored with onions and wild thyme “or piperna” and subsequently adjusted to taste by adding salt, oil, and vinegar. With a few modifications, this preparation was to enjoy a remarkable future in Italian cuisine and in the industry of preserved foods. The custom observed in ancient and medieval times, as well as during the Renaissance, of serving sauces as an accompaniment to “boiled foods or other dishes” – as Latini expresses it in this instance – facilitated the acceptance of the tomato by integrating it into an established gastronomic tradition. For the same reason, it gained widespread currency in Italian cooking in the eighteenth and nineteenth centuries. Panunto in Tuscany, Vincenzo Corrado in Naples, and Francesco Leonardi in Rome all include it in their recipe books.
This integrative model proved far more successful in Italy compared to partial replacement that using potatoes would have required. The tubers were only acclimatised very slowly and erratically in the kitchen systems.
The appearance of new, cheaper, and more readily available vegetables — both fresh and preserved (in the case of potatoes and tomatoes) — on the dinner table all year long favored this revolution. By the middle of the nineteenth century, the tomato was the basis for a sauce used universally in restaurants both humble and grand as an accompaniment to meat and also as a sauce for pasta dishes. Its stable, moderately acidic taste and its bright red color, undiminished by the process of preservation, ensured its success, and it became an ingredient that appeared equally in the dishes of the poor, the middle class, and the aristocracy. The story of the potato was somewhat similar. Although it had a poor reputation in terms of flavor and consistency, it was nonetheless easily transported, manipulated, and combined with other foods. So the potato too became an ingredient that was used across Italy’s social spectrum, though its cultivation was still unevenly distributed in the nineteenth century. Potatoes and tomatoes also raised the issue of territorial provenance, since they were ubiquitous and easily replanted and hence constituted culinary references that were not characteristic of a single place but could be considered universal.
For the spices, this is quite different. Medieval recipes from the peninsula are heavily dominated by marjoram and mint. And to a lesser extent by
basil, bay leaf, catnip, and, in Scappi’s work, pimpernel and wild thyme. […]
Italian recipe collections reveal an acceptance of nature that was unparalleled elsewhere, since they feature even ingredients such as mushrooms and truffles, the sign of an intense exchange of knowledge between the world of the peasants and urban and aristocratic environments. […]
The great recipe collections of the fifteenth and sixteenth centuries adopted and expanded this tradition. Cabbages, turnips, fennel, mushrooms, squash, let- tuce, parsley, and all sorts of herbs and legumes—such as broad beans and peas—are the basis of many preparations proposed by Maestro Martino (soups, torte, and fritters). Platina carefully offers detailed instructions on how to flavor lettuce, endives, oxtongue, moss rose, mallow, radishes, sassafras, pimpernel, and sorrel, as well as mixed salad:
A mixed salad is prepared with lettuce, oxtongue, mint, catnip, fennel, parsley, watercress, oregano, chervil, chicory, and dandelion greens (described by doctors as taraxacum and arnoglossa), wonderberry, fennel flowers, and various other aromatic herbs, well washed and drained. These are placed in a large dish and flavored with abundant salt. Oil is added, and vinegar sprinkled on top. The salad is then left to macerate for a short while. Because of the wild coarseness of the ingredients, one must be careful to chew thoroughly when eating. […]
In 1569 Costanzo Felici wrote: “Salad foods, according to those who live beyond the Alps, are almost exclusive to greedy Italians, who have appropriated the food of those base animals that eat raw greens.” His statement appears in a long letter to Ulisse Aldrovandi, titled De’ insalata e piante che in qualunque modo vengono per cibo del’homo (On salads and plants that in some way become the food of men), which constitutes a genuine treatise on gastronomic botany. We find many other famous examples of this type of document—part scientific treatise and part cookbook – in Italy.
The use of basil as 'typical Italian preference' is strange from an Italian perspective and a result of outside observation? Whereas other herbs and spices may grow well in colder climates or travel well in dried form, dried basil is one example that is in practice a whole different herb compared to fresh.
Quotes from Alberto Capatti & Massimo Montanari: "Italian Cuisine. A Cultural History", ('La cucina Italiana: Storia di una cultura', transl Aine O’Healy), Arts and Traditions of the Table, Columbia University Press: New York, 2003.