My favorite puttanesca is garlicky, spicy, and barely cooked. I prefer to treat it like a pico de gallo on top of pasta, just tossing it enough with the hot pasta to warm it up. Cooking it for a long time like you do other sauces makes it lose that special fresh quality (and really flattens out the garlic).
When you have a glut of fresh tomatoes, this is a great plan; if the tomatoes are not in perfect condition (usually when texture is grainy inside), you can also simmer it on the stove to disguise their flaws. Making the raw sauce and then canning it also works really well.
2 lbs. fresh tomatoes, cored and roughly diced
4-6 cloves garlic, smashed and minced
1/2 cup green olives, chopped
2 tablespoons capers
1/2 cup packed fresh basil leaves, chopped
olive oil, salt, and balsamic vinegar to taste
Combine all ingredients and refrigerate. Will keep up to one week; otherwise, can it or cook it and then it can be frozen.