Don’t bother peeling the tomatoes if you plan to put the sauce through a food mill. Furthermore, if you don’t mind a chunky tomato sauce, there is no need to peel the tomatoes or food-mill the sauce. For a classic, roux-thickened French tomato sauce (called Sauce Tomate), replace the olive oil with 2 tablespoons butter, then add 2 tablespoons flour to the softened vegetables and cook, stirring, until the flour is nutty and fragrant. Proceed as directed and pass the sauce through a food mill.
Heat in a large skillet over medium heat:
Add:
Cover, reduce the heat to low, and cook, stirring occasionally, until the vegetables are very soft, about 15 minutes. Add and cook, stirring, for 30 seconds:
Stir in:
Simmer, uncovered, crushing the tomatoes with a potato masher or a wooden spoon to break them up, until the sauce is thickened, 15 to 20 minutes. Pass through a food mill for a smooth sauce.