Preheat the oven to 400°F. Add the cherry tomatoes to an oven-safe baking dish, then drizzle with the olive oil and season with salt and pepper. Toss the tomatoes until they are evenly coated. Place the block of feta cheese in the center of the baking dish, nestling it among the tomatoes, and flip it once or twice so it’s lightly coated with the oil and seasoning as well. Bake in the preheated oven for about 35 minutes, or until the tomatoes have burst and the feta has softened and begun to melt. While the feta and tomatoes are baking, cook the pasta in a pot of generously salted boiling water according to the package directions until al dente. Drain the pasta, reserving ½ cup of the pasta water in case you need it to loosen the sauce. Once the feta and tomatoes are finished baking, add the minced garlic and chopped basil directly to the hot dish and stir until everything is well combined and creamy. Add the cooked pasta to the baking dish and toss to coat evenly. Garnish with extra fresh basil and serve immediately while warm.