Heat a large dry skillet over medium heat. Add the chopped walnuts and toast for 3-5 minutes, stirring frequently, until fragrant and lightly browned. Be careful not to burn them. Remove walnuts from the skillet and set aside.

Bring a large pot of heavily salted water to a rolling boil. Add the fettuccine and cook according to package directions until al dente. Before draining, reserve 1 to 1 1/2 cups of the starchy pasta water. Drain the fettuccine.

While the pasta cooks, return the same large skillet (no need to clean) to medium-low heat. Add the extra virgin olive oil, minced garlic, and red pepper flakes. Sauté for 1-2 minutes, stirring constantly, until the garlic is fragrant but not browned. Browning the garlic will make it bitter.

Add the drained fettuccine, chopped fresh parsley, and toasted walnuts to the skillet with the garlic and oil. Pour in about 1/2 cup of the reserved pasta water. Toss vigorously with tongs, allowing the starches from the pasta water and the oil to emulsify and create a light, glossy sauce that coats the fettuccine. Add more pasta water, a splash at a time, if the sauce seems too dry or if you prefer a looser consistency.

Taste the pasta and season with additional salt and freshly ground black pepper as needed. Serve immediately in warm bowls, topped generously with grated Parmesan cheese.