Bring a large pot of salted water to a boil and cook the fettuccine pasta according to package instructions until al dente. Reserve about 1 cup of pasta water, then drain the pasta in a colander.
In a large skillet, heat the olive oil over medium heat. Add the minced garlic and sauté for about 1 minute or until fragrant.
Add the shrimp to the skillet, seasoning with salt and pepper. Cook for 3-4 minutes, or until the shrimp turn pink and are cooked through, stirring occasionally.
Reduce the heat to low and pour in the heavy cream. Stir well to combine with the shrimp and garlic.
Gradually add the grated Parmesan cheese, stirring continuously until the cheese has melted and the sauce is creamy. If the sauce is too thick, add a bit of the reserved pasta water to reach the desired consistency.
Add the cooked fettuccine to the skillet, tossing to coat the pasta in the creamy sauce.
Serve immediately, garnished with freshly chopped parsley and additional Parmesan cheese if desired.