In a very large pot, bring 5 quarts water and 3 tablespoons salt to a boil. Add the pasta and cook until just al dente, about 1 minute less than the package directions. Occasionally give the pasta a stir so it doesn’t stick together. Scoop out and reserve 1 cup of the pasta water before draining the pasta.
Meanwhile, put a large skillet over low heat. Add the olive oil, garlic, and a pinch of salt. Cook until the garlic becomes aromatic, about 1 minute. Add the tomatoes with juices and red pepper flakes, increase the heat to medium-high, and cook for 2 minutes.
Add the cooked pasta to the pan, stirring the noodles into the sauce. Add a splash or two of the pasta water if the sauce looks too dry. Remove from the heat and stir in the butter, parsley, and parmesan. Serve immediately.