Cook the fettuccine pasta according to package instructions in a large pot of salted boiling water until al dente. Drain and set aside, reserving 1/2 cup of the pasta water.
In a large skillet, heat the olive oil 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 on each side until they turn pink and opaque. Remove the shrimp from the skillet and set aside.
In the same skillet, pour in the heavy cream and bring to a gentle simmer. Stir in the Parmesan cheese, salt, black pepper, and red pepper flakes (if using). Cook for 2-3 minutes until the sauce thickens slightly.
Add the cooked fettuccine and shrimp back into the skillet. Toss everything together, adding reserved pasta water a little at a time until the desired consistency is reached.
Serve immediately, garnished with chopped parsley.