Cut tomatoes in half horizontally. Squeeze out the seeds and discard, if you wish. Press the cut side of tomato against the large holes of a box grater and grate tomato flesh into a bowl. Discard skins. You should have about 4 cups.
Put tomato pulp in a low wide saucepan over high heat. Add salt, olive oil, tomato paste, garlic, basil and bay leaf. Bring to a boil, then lower heat to a brisk simmer.
Reduce the sauce by almost half, stirring occasionally, to produce about 2 1/2 cups medium-thick sauce, 10 to 15 minutes. Taste and adjust salt. It will keep up to 5 days in the refrigerator or may be frozen.