Bring a large pot of salted water to a boil. Add the pasta and cook until barely tender, about 4 minutes. Drain the pasta, reserving 1 cup of the cooking water, and set aside.
Set a 14-inch saute pan over medium-high heat and add the olive oil. Once the oil is hot, add the onion and cook until lightly caramelized and wilted, 3 to 4 minutes. Add the garlic and saute until fragrant, about 30 seconds. Add the crushed red pepper and saute briefly; then add the tomato sauce and tomato paste. Cook until the sauce has reduced by about 1/2, about 3 minutes. Add the shrimp to the sauce and cook for 2 minutes.
Add the pasta and the reserved cooking water to the pan, and cook until the pasta is heated through and coated with the sauce, 3 minutes. Season the pasta with the salt, and garnish with the parsley. Toss to combine, and serve with the grated cheese, if using and desired.