Bring a large pot of salted water to a boil. Add the fettuccine and cook until al dente, according to package instructions. Drain the pasta and set it aside.
In a large skillet, melt the butter over medium heat. Add the minced garlic and cook for about 1 minute, or until fragrant. Add the shrimp and cook until pink and cooked through, about 2-3 minutes per side. Remove the shrimp from the skillet and set them aside.
In the same skillet, pour in the heavy cream and bring it to a simmer. Add the grated Parmesan cheese, salt, and black pepper, and whisk the sauce until the cheese is melted and the sauce is smooth and creamy.
Add the cooked pasta to the skillet with the sauce and toss to coat the pasta evenly with the sauce.
Add the cooked shrimp to the pasta and sauce mixture, and gently toss to combine.
Divide the shrimp alfredo among serving plates and garnish with chopped parsley. Serve hot.