Thaw frozen shrimp in a colander under cool running water, then peel if needed and pat dry thoroughly. Dry shrimp will cook in the sauce without releasing excess water into the skillet.

Bring a pot of salted water to a boil and cook the fettuccine until al dente, following the package directions. Before draining, reserve a small cup of the hot pasta water for adjusting the sauce later.

Place the butter, softened cream cheese, heavy cream, chicken broth, and minced garlic in a skillet over medium heat. Stir as the butter melts and the cream cheese softens until the sauce looks smooth and the garlic smells fragrant.

Lower the heat as needed and let the sauce bubble gently for 5 minutes, stirring now and then. Look for light steam and small, quiet bubbles as the sauce reduces slightly without boiling hard.

Stir in the freshly grated Parmesan and cook for about 1 minute. The cheese should melt into a smooth sauce with no dry shreds remaining around the edges.

Add the prepared shrimp and cook for 5 to 6 minutes, stirring occasionally. The shrimp are ready when opaque and pink with a relaxed C-shaped curve.

Season with salt and pepper, then add the drained fettuccine and toss until coated. Add a splash of reserved pasta water if needed until the sauce has a silky sheen and clings evenly to the noodles.