The thing is tomatoes are a new world crop aka they came from the Americas same with potatoes, Italians have food that they made without using tomatoes for centuries. They could do a gimmick of making food closer to Roman style for a bit. Apparantly google says Northern Italian dishes don't use tomatoes as much as th Southern Italians.
Just research more Italian dishes and Ban and the main cast can learn more dishes and learn more about Italy and its cuisines.