In a 9x13 baking dish, add cherry tomatoes and garlic. Drizzle with olive oil, season with 1/2 tsp each salt and pepper and oregano. Toss well to combine.
Make a well in the center of the tomatoes to place the block of feta. Season feta with additional salt and pepper.
Bake for about 25 minutes or until tomatoes are bursting and feta turns golden on the edges.
While the feta is baking, prepare the pasta in salted water. Drain, reserving 1/2 cup of the cooking liquid.
Remove baking dish from the oven. Using a wooden spoon, gently stir the hot cheese with the tomatoes.
Add cooked pasta and 1/4 cup of the pasta water. Stir gently to coat the pasta with the sauce, adding additional pasta water if the mixture appears too dry.
Mix in basil. Taste for seasoning and adjust as desired. Serve with red pepper flakes.