Cook pasta according to the package directions, omitting salt and fat. Drain through a sieve over a bowl, reserving 1 cup cooking liquid. Return pasta to pan.
While pasta cooks, place tomatoes and next 6 ingredients (through black pepper) in a food processor; process until finely chopped.
Combine tomato mixture and the reserved 1 cup cooking liquid, stirring with a whisk. Add to pasta; toss well to coat. Sprinkle with feta.