Preheat oven to 400F. Place cherry tomatoes and garlic in a baking dish, toss with olive oil, oregano, red pepper flakes, salt, and pepper.
Nestle the whole block of feta into the center of the tomatoes.
Bake for 30-35 minutes until tomatoes have burst and feta is soft and lightly golden.
Cook pasta until al dente. Reserve 1 cup of pasta water before draining.
Mash the softened feta into the roasted tomatoes and juices with a fork.
Add drained pasta to the dish. Add pasta water gradually, stirring, until the sauce turns glossy.
Top with fresh basil and serve immediately.