Homemade Tomato Paste

Wash the tomatoes thoroughly. Remove stems and any blemishes. Cut the tomatoes into quarters and place them in a large pot. Cook over medium heat, stirring occasionally, until the tomatoes are soft and release their juices, about 30 minutes. Pass the cooked tomatoes through a food mill or blend them until smooth, then strain through a fine sieve to remove skins and seeds. Return the pureed tomato to the pot, add salt, and simmer gently over low heat, stirring frequently to prevent burning. Continue simmering until the mixture reduces by at least 75%, thickening into a deep, concentrated paste, which can take 1.5 to 2 hours. If desired, stir in olive oil and sugar for flavor. 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.