If using whole tomatoes, crush tomatoes with your hands or pulse in the food processor. Stir tomatoes in with vegetables or garlic depending on which version you're making. Use wine (or water) to rinse out cans and add it to the pot. Bring to a full simmer; reduce heat to medium-low and continue to simmer, uncovered, until sauce thickens and flavors meld, 15 to 25 minutes (see note below). Taste sauce, seasoning to taste with salt and pepper. Add enough tomato paste so that you’ve made a thick, full-bodied sauce. Simmer to blend flavors, a few minutes longer. Let cool and divide sauce among 3 to 4 quart-sized sealed containers. (Can be refrigerated a couple of weeks or frozen several months.)