Bring a large pot of water to a boil.
In a large skillet, heat the oil over medium heat till almost smoking. Add the garlic and cook until light golden brown, 30 seconds. Add half of the bread crumbs, chopped walnuts, and red pepper flakes and cook until lightly toasted, 3 to 4 minutes. Remove from the heat and set aside.
Cook the pasta in the boiling water according to the package directions. Right before the pasta is done, add 1/4 cup of the pasta cooking water to the pan with the walnut mixture.
Drain the pasta and add the pasta into the skillet with the walnut mixture, tossing to combine. Place the skillet over medium heat and toss until the pasta is lightly dressed with the sauce, about 1 minute. Add the parsley and cheese, stir through, pour into a heated bowl, sprinkle with the remaining bread crumbs, and serve immediately.