Cut the tomatoes into quarters and place them in a large pot.
4
Cook over medium heat, stirring occasionally, until the tomatoes are soft and release their juices, about 30 minutes.
5
Pass the cooked tomatoes through a food mill or blend them until smooth, then strain through a fine sieve to remove skins and seeds.
6
Return the pureed tomato to the pot, add salt, and simmer gently over low heat, stirring frequently to prevent burning.
7
Continue simmering until the mixture reduces by at least 75%, thickening into a deep, concentrated paste, which can take 1.5 to 2 hours.
8
If desired, stir in olive oil and sugar for flavor.
9
Transfer the thickened tomato paste to sterilized jars or containers, let it cool, then store in the refrigerator for up to a week or freeze for longer storage.