Bring a large pot of salted water to a boil and cook the fettuccine according to package directions until al dente; drain and keep hot.
In a large skillet over medium heat, melt the butter.
Add the minced garlic to the melted butter and sauté for about 1 minute until fragrant, taking care not to brown it.
Stir in the crab meat, heavy cream, grated Parmesan, salt, and black pepper; cook over medium-low heat, stirring constantly, until the sauce is warmed through and the cheese has melted and blended, about 2–3 minutes.
Add the hot, drained fettuccine to the sauce and gently toss until the pasta is evenly coated.
Serve immediately, garnished with the chopped fresh Italian parsley.