Step 1: Preheat your oven to 400°F (200°C).
Step 2: In a large, oven-safe baking dish (a 9×13 inch dish works well), add the cherry tomatoes. Drizzle generously with 3 tablespoons of olive oil. Add the minced garlic cloves, salt, and black pepper. Toss gently to coat the tomatoes evenly.
Step 3: Create a space in the center of the tomatoes and place the block of feta cheese directly in it. Drizzle the feta with the remaining 1 tablespoon of olive oil. Sprinkle a pinch of red pepper flakes over the feta and tomatoes, if desired.
Step 4: Bake in the preheated oven for 30 minutes, or until the tomatoes have burst and are slightly shriveled, and the feta is softened and lightly golden on top.
Step 5: While the feta and tomatoes are baking, cook your pasta according to package directions in a separate pot of boiling, salted water. Cook until al dente. Before draining, reserve about 1/2 cup of the starchy pasta water.
Step 6: Carefully remove the baking dish from the oven. Using a fork or a potato masher, gently mash the feta and burst tomatoes together until a creamy, rustic sauce forms. Stir everything together thoroughly.
Step 7: Add the drained, cooked pasta to the baking dish. Pour in about 1/4 cup of the reserved pasta water. Toss everything together until the pasta is well coated with the creamy feta and tomato sauce. Add more pasta water, one tablespoon at a time, if the sauce is too thick.
Step 8: Finally, stir in the fresh basil leaves. Serve immediately, garnished with extra fresh basil and a drizzle of good quality olive oil, if desired.