Bring a large pot of salted water to a boil and cook the fettuccine until al dente according to package directions.
While the pasta cooks, toast the walnuts in a dry skillet over medium heat for 2 to 3 minutes, stirring often, until fragrant.
Add the olive oil to the skillet, then stir in the garlic and red pepper flakes, cooking for about 30 seconds until aromatic.
Drain the pasta, reserving 1/2 cup of the cooking water.
Add the drained fettuccine to the skillet with the walnuts, parsley, and Parmesan, tossing to coat.
Add a splash of reserved pasta water as needed to help the sauce cling to the noodles. Season with salt and black pepper.
Serve immediately with extra Parmesan and parsley if desired.