Cook the pasta until al dente - according to package directions.
Drain and set aside. Reserve ½ cup of the pasta water.
Preheat oven to 400°F.
Dump the tomatoes and garlic into the baking dish.
Drizzle with olive oil and sprinkle with salt, pepper, oregano, and red pepper flakes. Toss to coat everything evenly.
Place the block of feta in the center of the baking dish surrounded by the tomatoes.
Bake for 30–35 minutes until the tomatoes are bursting and the feta is soft and slightly golden.
Remove and stir everything together; be sure to mash the feta and tomatoes into a creamy sauce. Add a splash of reserved pasta water to loosen the sauce if needed.
Toss the cooked pasta in the baking dish with the sauce until it is fully coated.