Bring a large pot of salted water to a boil.
Heat the olive oil in a large skillet over medium-high heat. Add the minced garlic and red pepper flakes and cook for 1 minute, stirring constantly to prevent the garlic from burning.
1 Tablespoon olive oil, 6 cloves garlic, 1/4 teaspoon crushed red pepper flakes
Add the diced tomatoes, salt, pepper, and white wine or chicken broth (I just used the broth). Bring everything to a simmer for about 5 minutes, stirring occasionally.
7 medium roma or plum tomatoes, Salt & pepper, 1/2 cup chicken broth
While the sauce simmers, cook the pasta according to the package directions until al dente (typically 3-4 minutes). Reserve about 1/2 cup of the starchy pasta water, then drain the pasta.
8-12 ounces angel hair pasta
Add the shrimp to the skillet and nestle them in the sauce. Cook for 3 to 4 minutes, turning the shrimp halfway through, until the shrimp turns pink. Be sure not to overcook the shrimp though or they will be tough and rubbery.
1 pound medium raw shrimp
Add butter and basil, and stir until the butter melts. Taste the sauce and add salt and pepper, as needed.
1 Tablespoon salted butter, 1/4 cup fresh basil
Add the cooked pasta to the pan and toss to coat. Add as much of the reserved pasta water as you would like to moisten the pasta if needed, then serve with additional chopped basil and the Parmesan cheese sprinkled on top.
1/2 cup freshly grated Parmesan cheese