Bring a large pot of salted water to a boil. Add the fettuccine (or spaghetti) and cook according to package instructions until al dente, usually about 8-10 minutes. Reserve about 1 cup of pasta water, then drain the pasta using a colander.
While the pasta is cooking, heat the olive oil in a large skillet over medium heat. Add the minced garlic and sauté for about 1 minute, until fragrant.
Add the shrimp to the skillet and cook for 2-3 minutes, until they turn pink and opaque. Season with salt, black pepper, and red pepper flakes, if using.
Reduce the heat to low, then pour in the heavy cream and stir well to combine. Gradually add the Parmesan cheese, mixing until the sauce is smooth and creamy. If the sauce is too thick, add reserved pasta water a little at a time until you reach your desired consistency.
Add the drained pasta to the skillet and toss until fully coated in the creamy shrimp sauce. Cook for an additional 1-2 minutes to heat through.
Serve immediately, garnished with fresh parsley.