Bring a large pot of salted water to a boil over high heat. Cook pasta according to package directions and drain, reserving about 1 cup of pasta water.
In a large pan big enough to hold the pasta, melt butter over medium heat, then stir in garlic and sauté about 1 minute till soft. Stir in heavy cream and bring to a low simmer, stirring often with a wood spoon till thick and leaves a line in the pan when stirred (about 5-6 minutes). Add in the cooked pasta, using tongs to toss with the cream sauce till it's well-coated.
Add in the mozzarella cheese, and continue to toss the pasta with the tongs till the cheese has melted. Add ¼ cup of hot pasta water if more liquid is needed to keep the pasta creamy and glossy. Taste and adjust any seasonings, adding salt, pepper, or a pinch of nutmeg as needed. Top with parsley, if desired.
Serve immediately and warm! The longer the pasta sits and cools, the more the cheese will begin to firm up again.
