Add the tomatoes to a 9-inch x 13-inch baking dish and add the olive oil. Toss to coat the tomatoes. Place the block of feta into the dish arranging the tomatoes around the cheese. Brush some of the olive oil from the dish on top of the feta.
Bake for 30-35 minutes until the tomatoes begin to burst open.
While the cheese bakes, bring a large pot of salted water to a boil. Add the pasta and cook according to the package directions until al dente. Drain and set aside. *Reserve 1/2 cup pasta water before draining. You may not need it later, but better to have some on hand in case.
Remove the baking dish from the oven. Add the garlic and mix well. Then stir in the cooked pasta until it's well coated. If needed, add splashes of pasta water to make a creamier sauce. (You may not need any pasta water.)
Season the pasta with salt and pepper to taste, and then sprinkle with chopped basil before serving warm.
Notes
If you can't find a 16-ounce block of feta, you can use two 8-ounce blocks instead.