Preheat the oven to 400°F.
In a large, ovenproof baking dish, combine the cherry tomatoes, minced garlic, and extra-virgin olive oil. Toss gently until the tomatoes are evenly coated. Season lightly with salt, black pepper, and red pepper flakes.
Place the feta block in the center of the tomato mixture, turning it once or twice so it’s lightly coated in oil and seasoning. Drizzle a little extra oil over the feta, if desired.
Bake, uncovered, for 30-35 minutes, or until the tomatoes are blistered and soft, and the feta is golden brown on top.
Meanwhile, cook the pasta in a large pot of salted boiling water until just al dente, about 1-2 minutes less than the package directions state. Reserve about 1/3 cup of the pasta cooking water before draining.
Remove the baking dish from the oven. Use a spoon to gently mash the tomatoes and feta together in the dish to create a creamy sauce. If the mixture looks dry, stir in a bit of the reserved pasta water until it reaches your desired consistency.
Add the drained pasta directly to the baking dish, tossing well to coat with the feta-tomato sauce. Taste and adjust seasoning with more salt or pepper as needed.
Garnish generously with fresh basil leaves and serve warm.