Core and halve tomatoes. Remove seeds (either scoop them out with a spoon or hold a half in your hand and squeeze out the seeds) and cut tomatoes into 1/2-in. dice. Set aside.
Thinly slice garlic. In a 10- to 12-in. frying pan over low heat, cook garlic in olive oil until it is soft and fragrant, about 5 minutes.
Add tomatoes and 1 tsp. salt and increase heat to medium-high. Cook until tomatoes give off their liquid and start to bubble. Reduce heat to medium-low or low, so the sauce gently simmers. Cook, uncovered and undisturbed, until oil separates from the sauce and most of the liquid has evaporated, about 30 minutes.
Meanwhile, chop basil. When sauce is done, stir in basil and add salt to taste.
Butter it up: Use unsalted butter in place of the olive oil and a chopped medium onion in place of the garlic.
Explore the herb patch: Try 1/2 to 1 tsp. minced fresh oregano, marjoram, rosemary, or thyme instead of the basil.
Add some heat: Toss in 2 or 3 dried whole arbol chiles with the garlic for a slightly spicy version. Remove chiles before serving.
Pick more produce: At the beginning of step 3, add one skinned and chopped medium eggplant and cook until soft, about 10 minutes, before adding the tomatoes.
Note: Nutritional analysis is per 1/2 cup.