Preheat oven to 400 degrees. Combine the tomatoes, ¼ cup olive oil, garlic, and ½ teaspoon salt in a 9 by 12 (or similar) baking dish. Toss to coat. Place the feta in the middle of the dish, pushing the tomatoes to the side so that the cheese is sitting right on the baking dish and not on the tomatoes. Sprinkle on the pepper and red pepper flakes. Pour ¼ cup of olive oil all over. Bake for 40 minutes or until the tomatoes burst.
While the tomatoes and cheese bake, bring a large pot of heavily salted water to a boil. Cook the pasta according to the package directions. Drain, reserving some of the pasta cooking liquid.
When the tomatoes and cheese are done, mash them together with a fork. Add the pasta and mix, adding some of the pasta water if the pasta seems too dry. Top with fresh basil and serve.