In a medium nonreactive pan / saucepan heat 3 tbsp of olive oil over medium-low heat. Add the chopped onions and cook until light golden color , 10-12 minutes.
Add the garlic and saute until the garlic is fragrant & tender, about 1 minute.
Transfer the chopped tomatoes to the pan. Bring the sauce to simmer. Cook over low heat ,stirring from time to time, about 25-30 minutes. Cooking time depends on the quality of the tomatoes. Also tomatoes's moisture content can increase of decrease the cooking time.
Now it is time to add the basil chiffonade, salt & black pepper. Simmer another 2-3 minutes.
Puree the sauce using a food mill with a coarse disk to make a rough puree. You can skip this step if you need the chunky sauce.
Use the sauce immediately or refrigerate for later use.