Best Fettuccine Alfredo

Name: Best Fettuccine Alfredo
Ingredients: 1 pound dried fettuccine; 2 tablespoons kosher salt, plus 1/2 teaspoon, plus more as needed; 8 tablespoons (1 stick) unsalted butter, cut into cubes; 1 large garlic clove, halved lengthwise and finely sliced so you end up with semi-circles about 1/4-inch thick; 1/2 teaspoon freshly cracked black pepper (I do this in a mortar and pestle); 1 cup heavy whipping cream; 2 cups firmly packed Microplaned* Parmesan and/or Pecorino Romano (I like a 50-50 mix, and prefer Locatelli Pecorino), plus more for serving; 1 small bunch parsley, sliced into thin ribbons, for serving