I recall that when I was in Chiavenna (in the north, bordering Switzerland) there is a valley with a large chestnut forest. Chestnuts used to be a staple in that region.
You can also read up on the ancient roman diet, there are many sources on that.
Fish, bread, olive oil, beef, pork, wine, basically the ancient roman diet continued until the crusades at least.
There are records of pasta being prepared in Italy from back to the first century AD
Come to think of it... those were Romans, not Italians. Italy didn't exist until its unification in 1861, all these new world veggies are entirely "traditional Italian"...