Bring a large pot of salted water to a boil. Cook fettuccine according to package directions until al dente. Reserve 1/2 cup of pasta water before draining.
Pat shrimp dry with paper towels and season with a pinch of salt and pepper.
Heat olive oil in a large skillet over medium-high heat. Add shrimp in a single layer and cook for 1-2 minutes per side until pink and opaque. Remove shrimp from the skillet and set aside.
In the same skillet, melt butter over medium heat. Add minced garlic and sauté for 1 minute until fragrant.
Whisk in heavy cream and bring to a gentle simmer. Let simmer for 3-5 minutes until slightly thickened.
Lower heat to medium-low and whisk in grated Parmesan cheese until melted and smooth. Season with salt, pepper, and nutmeg.
Add the cooked pasta and sautéed shrimp to the sauce. Toss to coat evenly. If sauce is too thick, add reserved pasta water 1 tablespoon at a time until desired consistency is reached.
Garnish with fresh parsley and serve immediately.