Bring a pot of salted water to a boil and cook the fettuccine according to package directions; 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 but not browned.
Stir in the crab meat, heavy cream, grated Parmesan, salt, and black pepper; heat gently while stirring constantly until the cheese melts and the sauce is smooth and warmed through.
Add the hot, drained fettuccine to the skillet and toss lightly to coat the pasta evenly with the sauce.
Serve immediately and garnish with the chopped fresh Italian parsley.