Cook the fettuccine according to package directions until al dente. Reserve 1 cup of the pasta water before draining.
While the pasta cooks, melt the butter in a large skillet over medium heat. Add the minced garlic and cook for 1 minute until fragrant; do not let it brown.
Add the shrimp to the skillet. Cook for 2 to 3 minutes per side until pink and opaque. Remove the shrimp from the skillet and set aside.
Reduce the heat to low. Pour the heavy cream into the skillet. Let it warm through for 2 minutes, stirring occasionally.
Gradually whisk in the grated Parmesan cheese until the sauce is smooth and thickened. Do not let the sauce boil.
Stir in the salt, pepper, and nutmeg. If the sauce is too thick, add reserved pasta water, one tablespoon at a time, until you reach a silky consistency.
Return the cooked shrimp to the sauce. Toss with the drained fettuccine until everything is coated evenly.
Serve immediately, garnished with fresh parsley and extra Parmesan cheese.
Notes
Use freshly grated Parmesan cheese for the best melting and flavor; pre-shredded cheese often contains anti-caking agents that prevent a smooth sauce.
Keep the heat low when adding the cheese to prevent the sauce from separating or becoming grainy.
For extra richness, you can add 1/4 cup of dry white wine after cooking the garlic, letting it reduce slightly before adding the cream.