In this recipe, plum tomatoes (fresh or canned) are simmered slowly without salt, oil, garlic, or onion, to keep their natural flavor intact. If using fresh tomatoes, they should be very ripe, fleshy, and sweet plum tomatoes. If using canned tomatoes, use imported italian plum tomatoes, which are sweeter and more fleshy than most domestic varieties (Redpack brand is an exception). The skin is left on the tomatoes to impart additional taste and body to the sauce. The carrot is added in place of sugar to compensate for excess acidity in the tomatoes. Extra-virgin olive oil is mixed in after the sauce is cooked so that its raw, fruity flavor comes through clearly. This sauce is enormously versatile on the antipasto table when a tomato sauce is required to add moisture and flavor and a heavier sauce would overwhelm. It is just the right salsa on which to lay cold meatloaf (polpettone) slices, or with which to anoint baked stuffed vegetables. I also like to use it on thin dried pasta such as spaghettini and capellini because its light, sieved texture marries well with such delicate cuts. But it goes well with just about all pasta cuts, as well as with homemade fresh potato gnocchi.