Cook the fettuccine according to package directions until al dente. Reserve 1 cup of the pasta water before draining. Set the pasta aside.
Season the shrimp lightly with salt and pepper.
Heat the olive oil and 2 tablespoons of the butter in a large skillet over medium heat. Add the shrimp and cook for 2 to 3 minutes per side until pink and opaque. Remove the shrimp from the skillet and set aside.
Add the remaining 2 tablespoons of butter to the same skillet. Add the minced garlic and cook for about 1 minute until fragrant. Do not let the garlic brown.
Pour in the heavy cream. Bring the mixture to a gentle simmer, stirring constantly. Reduce the heat to low.
Slowly whisk in the grated Parmesan cheese, a little at a time, until the sauce is smooth and thick. Stir in the salt, pepper, and nutmeg. If the sauce seems too thick, add a splash of the reserved pasta water until you reach a silky consistency.
Add the cooked pasta and the cooked shrimp back into the skillet with the sauce. Toss gently to coat everything evenly. If needed, add more pasta water to loosen the sauce.
Serve immediately, garnished with fresh parsley and extra Parmesan cheese.
Notes
For the silkiest sauce, use freshly grated Parmesan cheese; pre-shredded cheese contains anti-caking agents that can make the sauce grainy.
Do not boil the sauce once the cheese is added, as this can cause the sauce to separate or break. Keep the heat low.
If you prefer a tangier flavor, add 1 teaspoon of lemon juice at the very end.