In a 13x9-inch baking dish, combine the tomatoes, garlic and ¼ cup olive oil. Place the block of feta in the center, moving the tomatoes so the cheese is sitting on the pan bottom. Drizzle the feta with the remaining oil and sprinkle with salt and pepper. Bake until the tomato skins start to split and the garlic has softened, 30 to 40 minutes.
Meanwhile, cook the pasta according to package directions for al dente. Drain reserving 1 cup pasta water.
Stir the feta mixture, lightly pressing the tomatoes, until combined. Add the pasta and toss to combine. Stir in enough reserved pasta water to achieve the desired consistency. Sprinkle fresh basil on top.