Heat 3 tablespoons of the olive oil in a medium (10-inch) saute pan. Add the onion and saute over medium-low heat for 5 minutes, stirring occasionally, until very tender but not browned. Add the garlic and saute for 1 more minute. Stir in the tomatoes, 1 teaspoon salt, and 1/2 teaspoon pepper and cook over medium-low heat for 10 to 15 minutes, stirring occasionally, until the liquid evaporates and the tomato sauce thickens slightly. Off the heat, stir in the vinegar and basil.