Bring a pot of water to a boil and salt lightly. Add the pasta and cook until not quite al dente and still quite chewy, 5 to 6 minutes. Reserve 2 cups of the pasta water, then drain.
Melt 3 tablespoons of the butter in a large skillet over medium heat. When melted, add the garlic and 1 1/2 cups of the pasta water and bring to a simmer. Grind in a generous amount of pepper. Add the pasta and remaining 3 tablespoons butter to the skillet. Stir to combine and let the pasta start to simmer. Begin adding the Parmesan a handful at a time, tossing the pasta with each addition and adding more pepper if desired. Remove from the heat and continue to toss the pasta until well coated, thinning with the extra pasta water if needed. Taste and add more pepper if desired. Divide among bowls and garnish with the parsley. Serve with more Parmesan on the side.