Add about 1/2 cup olive oil and 1 tsp. salt to the tomatoes and bring them to a boil over high heat. Cook, stirring, just until tomatoes soften, about 2 minutes. This brief cooking helps break the tomatoes down a bit and makes them easier to run through a food mill or sieve.
Note: If you have a tomato mill or food mill and a strong arm, you can skip this initial cooking step, if you like.