Set a large pot of water to boil, generously seasoned with salt, over high heat. Cook the spaghetti according to package instructions, until just shy of al dente.
While the pasta is cooking, prepare the sauce by combining the olive oil, garlic, red pepper flakes and a pinch of salt in a large skillet. Bring to the stove, over medium low heat, and cook slowly, letting the oil absorb the flavors from the garlic and pepper flakes.
When the pasta is almost al dente, transfer it to the skillet with the flavored oil along with 1/2 cup of the pasta water. Turn the heat back to medium high and cook, stirring and tossing rapidly until the pasta is al dente and the sauce has thickened/emulsified and coats the pasta. If you want, you can add some more olive oil.
Remove from heat, add the chopped parsley and serve with Parmigiano Reggiano on the side.