Cook pasta according to package directions. Drain, reserving 1 cup of the cooking liquid.
While pasta is cooking, place the tomatoes and the next 6 ingredients (through the pepper) in a food processor. Pulse until finely chopped.
Place tomato mixture in a serving bowl. Whisk together with 1/2 cup of the reserved cooking liquid, adding more as necessary until you reach the desired consistency. Add the pasta and feta cheese; toss to combine.