Bring a large pot of salted water to a boil. Cook the pasta until al dente, about 8-10 minutes. Reserve 1/2 cup pasta water, then drain.

Melt the butter in a large skillet over medium heat. Add the garlic and cook 1 minute until fragrant.

Whisk in the flour and cook 1 minute. Slowly pour in the milk while whisking, then cook 3-5 minutes until thickened.

Reduce heat to low, stir in Parmesan, salt, pepper, and nutmeg until melted, about 1 minute.

Add the drained pasta to the sauce and toss well, adding pasta water as needed to loosen. Serve immediately with extra Parmesan and parsley.