Bring 6 quarts of water to a boil in a large pot and add 3¬†tablespoons kosher salt.
Meanwhile, combine the olive oil and garlic in another large¬†pot and cook over medium heat, stirring occasionally, until¬†the garlic is just beginning to brown lightly, 2 to 3 minutes.
Stir in the red pepper flakes and parsley and remove from¬†the heat.
Drop the pasta into the boiling water and cook until just al¬†dente. Drain, reserving about ¬Ĺ cup of the pasta water.
Return the garlic oil to medium heat, add the pasta and ¬ľ¬†cup of the reserved pasta water, and stir and toss over¬†medium heat to coat the pasta well (add a splash or two¬†more of the reserved pasta water if necessary to loosen the¬†sauce). Serve immediately, with grated Parmigiano on the¬†side.