Preheat oven to 400°F (200°C).
Place cherry tomatoes in a baking dish. Add garlic, oregano, red pepper flakes, salt, and pepper. Drizzle with olive oil and toss gently.
Place the feta block in the center of the tomatoes and drizzle lightly with olive oil.
Bake uncovered for 25–30 minutes, until tomatoes burst and feta is soft.
While baking, cook pasta in salted water until al dente or desired tenderness. Reserve ½ cup of pasta water, then drain.
Remove the baking dish from the oven and mash the feta and tomatoes together until creamy.
Add cooked pasta to the dish, tossing to coat. Add reserved pasta water a little at a time if needed for a silky sauce.
Garnish with fresh basil and serve warm.