Place the minced onion, garlic, celery, carrots, whole canned tomatoes, basil, olive oil and 2 teaspoons kosher salt in a large saucepan.
Simmer for 45 minutes with a lid ajar, stirring occasionally.
Remove from the heat and rest 5 minutes. Discard the basil leaves. Carefully transfer the mixture to a blender. Add the sugar and several grinds black pepper. Blend until smooth (or pulse for a chunkier texture). Taste and add more salt as desired (we typically add another 1/2 teaspoon or more).
Serve with pasta: for 1 pound pasta, stir in 4 cups sauce, then add more to taste if desired. Top generously with grated Parmesan or grated Pecorino cheese before serving (or, stir it into the warm sauce). Store refrigerated for up to 5 days or frozen for up to 6 months.