Put the oil and onion in a large saucepan and place over medium heat. Cook until the onion is soft, about 5 minutes, stirring. Add the garlic and stir until it smells good, 15-20 seconds.
Add the tomatoes, 1-2 teaspoons salt, black pepper and sugar to the pan. Bring to a simmer, breaking up the tomatoes into pieces with a spoon. Cook uncovered 20 minutes or so, until the sauce has thickened slightly.
Taste for seasoning - add more salt or pepper to taste.
Meanwhile, bring a large pot (5-6 quarts) water to a boil and add 3 tablespoons salt. Cook the pasta until al dente, according to package directions. Drain well.
Put the pasta in a large serving bowl and ladle over about half the sauce. Top with the cheese and toss to coat. Sprinkle the basil over. Serve with additional cheese.
The sauce makes enough for 2 pounds of pasta. It will keep refrigerated 5 days or frozen for up to 2 months.For a smoother sauce, use a handheld immersion right in the pot or let the sauce cool sllightly and briefly pulse in a blender.Pomodoro sauce variations:
Add crushed red pepper to taste along with the onions
Swirl in 1 or 2 tablespoon butter to the finished sauce for extra richness.
To make pomodoro sauce with fresh tomatoes: You'll need 3 pounds of fresh, ripe tomatoes for this sauce. Dip them in boiling water for 30 seconds and slip the skins off. Chop them and proceed with the recipe.