Bring a large pot of salted water to a boil and cook the fettuccine according to package directions until al dente. Drain and set aside, reserving a little pasta water if desired.
In a medium saucepan over medium heat, melt the butter. Add the minced garlic and cook, stirring frequently, until fragrant, about 1 minute.
Stir in the flour and cook briefly to form a paste. Gradually whisk in the milk and continue whisking until the mixture thickens into a smooth sauce.
Reduce heat to low and stir in 1 cup of the Parmesan, the cream cheese, and the salt until the cheeses melt and the sauce is smooth.
Add the hot, cooked fettuccine to the sauce and toss to coat, adding a splash of reserved pasta water if needed to loosen the sauce.
Serve immediately with the remaining Parmesan sprinkled on top, chopped flat-leaf parsley, and freshly ground black pepper to taste.