Preheat an oven to 300°F.
Remove and discard stems and any damaged parts from the tomatoes. Roughly chop the tomatoes and put them in a large pot. This can be a very rough chop - you just want to get the tomatoes started to break down.
Note: If you're working with tomatoes than contain a lot of juice, you might want to halve them and squeeze out and discard the seeds and watery juice in the center to help speed up the concentration process that will turn tomato puree into tomato paste.