Bring a large pot of salted pasta water to a boil, then add your pasta and cook to al dente, according to package directions. Drain and toss with olive oil to prevent sticking.
Heat the oil in a large skillet over medium high heat. Add the sliced leeks and saute for 2 minutes. Add the sliced mushrooms and saute until softened and browned, another 5-6 minutes. To assist with browning, only stir the mushrooms once every few minutes. Stir in the minced garlic. Season with salt and pepper.
Stir in the broth and cream and allow the mixture to simmer for 5-7 minutes, or until thickened slightly. Stir in the Parmesan cheese and parsley and mix until cheese is melted. Add red pepper flakes, salt, and pepper to taste.
Toss the pasta with the sauce and stir to coat. Serve immediately with additional Parmesan and parsley, if desired.
