Bring a large pot of water to a boil, and salt the water well (about 2 tablespoons of kosher salt). Add the pasta and cook according to package instructions until just al dante or a little before (mine took about 9 minutes). Before you drain the pasta, make sure to reserve about 1 ½ cups of the pasta cook water.
Meanwhile, 4 minutes after you add the pasta to the boiling water, warm the olive oil in a large pan over medium heat. Add the garlic and cook for about 2 to 3 minutes, tossing regularly until the garlic is just turning golden brown (manage the heat well so that the garlic does not overcook). Add the red pepper flakes and toss for 30 seconds or so. If the pasta is not ready, move the oil off the heat for now.
Carefully ladle the reserved pasta cooking water in the pan. Bring to a simmer until the liquid reduces by about ⅓.
Add the cooked pasta and toss around for a couple of minutes. Turn the heat off and add the parmesan and parsley. Toss to combine.
Allow the pasta a couple more minutes to rest and absorb the sauce. Serve with more Parmesan and red pepper flakes to the side.