Wash the tomatoes well and chop them roughly, removing any bad spots and stems. Place them directly into a very large pot.
Roughly cut the carrot, onion, and celery and add to the pot. Wash the herbs and remove large, stalky stems before adding directly in with the other vegetables.
Turn the burner on medium-low and gently start to warm the tomatoes. The juices will start to slowly release, cooking the other vegetables as they do. Season with two teaspoons of salt and add the olive oil. Mix well.
Allow the tomatoes to simmer slowly, uncovered, stirring from time to time to help break up the tomatoes and keep it from sticking to the bottom of the pot. At this point, the longer it cooks, the better it is. You want the sauce to be thick yet not overly dense. If your tomatoes are very juicy (which they should be), the sauce may reduce in volume anywhere from ⅓ to ½! This may take several hours. Season for salt before passing the fresh tomato sauce through a food mill.
Set the food mill over a large bowl and add several scoops of fresh pomodoro sauce. Turn the mill, back-turning from time to time to clear the holes, until all the juices and sauce has been squeezed from the fibers, seeds and skin. Remove the scraps and carry on in this fashion.
Freeze or can according to your personal preference or space allowance.