Pour just enough olive oil into a large pot to coat the bottom; place over medium heat. Cook and stir sweet onion in the pot until it releases some moisture, 1 to 2 minutes. Stir garlic with the onion; cook another 1 minute. Remove pot from heat immediately.
Process the tomatoes in a large food mill using medium holes; grind directly into the pot. Bring the tomato mixture to a light simmer over medium-low heat; season with oregano, salt, and pepper. Allow the mixture to simmer 1 hour, stirring regularly.
Stir basil leaves into the sauce. Simmer 1 hour more, again stirring regularly.
