1. Preheat oven to 250 degrees. Heat oil in a large, heavy saucepan over medium heat. Add tomatoes and salt. Cook, stirring occasionally, until the tomatoes have broken down, 5 to 10 minutes.

2. Pass tomatoes through a food mill or a fine sieve; discard seeds and skin.

3. Pour sauce evenly onto a rimmed baking sheet. Bake until mixture begins to thicken, about 3 hours. Stir with a rubber spatula to redistribute, and spread evenly on sheet. If tomato mixture no longer fills sheet, transfer to a smaller sheet.

4. Bake until liquid has completely evaporated and mixture has thickened, about 3 hours more, stirring every 30 minutes.