Place large saucepan on stovetop over medium-high heat. When saucepan is warm, add 2 tablespoons olive oil. Swirl and tilt pan as needed to distribute oil across surface of saucepan, and continue heating saucepan until oil is hot and shimmery.
When oil is ready, add 1 medium onion (chopped) to saucepan and stir to incorporate onion into oil. Sauté onions, stirring occasionally, 8 to 10 minutes or until onions are very soft.
Once onions have softened, reduce heat under saucepan to medium. Add 3 large cloves garlic (minced) and stir to incorporate. Sauté garlic 60 seconds or until just fragrant, stirring constantly.
When garlic is fragrant, add 2 28-ounce cans whole peeled San Marzano tomatoes and stir to incorporate. Increase heat under saucepan to high and bring mixture to boil, stirring occasionally.
When tomato mixture begins to boil, immediately reduce heat under saucepan to low. Simmer mixture 20 minutes, stirring occasionally and breaking up tomatoes with wooden spoon or spatula.
After 20 minutes, add ¼ cup chopped fresh basil leaves to saucepan and stir to incorporate. Simmer mixture 5 minutes more, stirring occasionally.
After 5 minutes, remove saucepan from heat. Add 1 ½ teaspoons kosher salt and ½ teaspoon freshly ground black pepper, then stir to incorporate. Let mixture cool slightly.
When mixture has cooled slightly, insert immersion blender into saucepan. Purée mixture until sauce is thick and mostly smooth. See Notes below if using standard blender.
When satisfied with consistency, taste sauce and adjust salt and/or pepper if needed. When satisfied with flavor of sauce, add cooked pasta of choice to saucepan and stir to cover pasta in pomodoro sauce.
Portion pasta and pomodoro sauce evenly between serving bowls or plates, top with grated parmesan if desired, and serve immediately.