Bring a large pot of salted water to a boil. Cook fettuccine according to package directions until al dente. Reserve 1 cup of pasta water, then drain the pasta.

While pasta cooks, pat shrimp dry with paper towels. Toss with olive oil, salt, pepper, and paprika. Heat a large skillet over medium-high heat. Add shrimp in a single layer and cook for 2 minutes per side, or until they reach an internal temperature of 145°F (63°C), pink and opaque. Remove shrimp to a plate.

In the same skillet, reduce heat to medium. Melt butter, then add minced garlic and sauté for 30 seconds until fragrant. Pour in heavy cream, stirring constantly. Bring to a gentle simmer and cook for 2 minutes. Reduce heat to low, then whisk in Parmesan cheese and nutmeg (if using) until smooth. Season with salt and pepper to taste.

Add drained pasta and cooked shrimp to the skillet. Toss gently to coat everything in the sauce. If sauce is too thick, add reserved pasta water a tablespoon at a time until desired consistency. Sprinkle with fresh parsley and serve immediately.