Transfer pasta to the pan with the sauce. Stir in as much of the cooking water as necessary to just loosen the sauce and get the pasta coated. Transfer to a warmed shallow serving bowl or platter; sprinkle with ¼ cup cheese. Serve immediately with additional cheese on the side.
Homemade tomato purée is easy to make. For 1 cup, briefly dip 6 big tomatoes in boiling water; peel, halve, seed and roughly chop. Whirl in a blender until smooth. [Here's an alternate method.]