Put a large pot of salted water on for the pasta. Meanwhile, prepare your sauce. In a large skillet, heat 1/4 cup of the olive oil. Add the garlic and cook until just fragrant, about 1 minute or less. Add the tomatoes and cook them for 3 to 5 minutes, just until they begin to release some of their juice.
Cook the pasta in the pot of salted boiling water for 12 to 13 minutes until al dente. Drain the pasta. Add the pasta and basil to the pan with the tomatoes and toss. Season, to taste, with salt and freshly ground black pepper.
Serve the pasta in bowls, equally distribute the fresh mozzarella and grated Parmesan between the bowls. Drizzle the remaining olive oil over the bowls of pasta and serve immediately.