Heat oil in large skillet over medium-high heat. Add mushrooms and nutmeg. Saute until mushrooms are brown and tender, about 10 minutes. Add in garlic and saute for 2-3 more minutes. Sprinkle with salt and pepper. Stir in cream. Remove from heat.
Cook pasta in large pot of boiling salted water until tender but still firm to bite. Drain, reserving 1/2 cup cooking liquid. Return pasta to pot. Add mushroom mixture, salmon, 1 1/2 cups cheese, 1/2 cup parsley and reserved cooking liquid. Toss over medium-high heat until sauce coats pasts. Season with salt and pepper. Mix in remaining 1/4 cup parsley. Transfer pasta to bowl. Serve with remaining cheese.