Step 1: Bring a large pot of generously salted water to a rolling boil. Add the pasta and cook according to package directions until al dente. Before draining, reserve about 1 cup of the starchy pasta water. Drain the pasta and set aside.
Step 2: While the pasta is cooking, heat the olive oil in a large skillet or sauté pan over medium heat. Add the minced garlic and red pepper flakes. Sauté for 1-2 minutes, stirring constantly, until the garlic is fragrant but not browned. Be careful not to burn it.
Step 3: Add the halved cherry tomatoes to the skillet. Cook, stirring occasionally, for 8-10 minutes, or until the tomatoes begin to soften and burst, releasing their juices. You can gently press some of them with the back of your spoon to help them along.
Step 4: Pour in about 1/2 cup of the reserved pasta water into the skillet. Stir well, scraping up any browned bits from the bottom of the pan. This will help create a flavorful, emulsified sauce.
Step 5: Add the drained pasta directly to the skillet with the tomato sauce. Stir in the torn fresh basil leaves and the grated Parmesan cheese. Toss everything together until the pasta is thoroughly coated in the sauce. If the sauce seems too thick, add more pasta water, a tablespoon at a time, until you reach your desired consistency.
Step 6: Season the pasta with salt and freshly ground black pepper to taste. Serve immediately, garnished with extra fresh basil leaves and a sprinkle of additional Parmesan cheese.