This makes enough sauce for about 1 kilogram (2-plus pounds of pasta). Most often this sauce is used as the base for other sauces. You can make it in larger quantities and freeze it for future use. While I prefer to pass the tomatoes through a food mill to remove the seeds and the occasional hard bit of tomato, you can skip this step. Just add the tomatoes to the sautéed vegetables, mashing them with a potato masher, and proceed as written. Since this sauce cooks quickly it is especially important that the vegetables be very finely diced.
Sweat the onion, carrot and celery, with a large pinch of salt, in the olive oil until soft and the onion is golden, without browning, approximately 15 minutes.
Meanwhile, pass the tomatoes through a food mill.
There should be very little residual in the food mill.
Add the tomatoes to the vegetables. Season with salt and pepper.
Simmer, partially covered approximately 15 minutes.
Cool slightly and blend with an immersion blender or jar blender. Adjust salt and pepper.