Bring a large pot of salted water to a boil over high heat. Add fettuccine and cook according to package instructions.
Melt butter in a large skillet over medium heat. Add minced garlic and cook for 1 to 2 minutes, then stir in the heavy cream.
Simmer the heavy cream for 5 to 8 minutes until reduced. Whisk in half of the parmesan cheese until smooth and continue whisking over heat until completely melted.
Reserve a portion of the pasta water to thin the sauce if necessary.
Toss the fettuccine with the alfredo sauce and half of the parmesan cheese. Garnish with the remaining parmesan and add reserved pasta water as needed to reach the desired consistency.
Garnish with Italian parsley if desired.