Cook fettucine according to package directions; drain, keep warm.
While pasta is cooking, melt the butter in a large skillet over medium high heat. Add the green onions and garlic. Cook, stirring occasionally for 2 minutes. Add the whipping cream and boil rapidly until slightly thickened.
Add the hot pasta to the cream mixture, toss lightly. Add 1/2 cup of the cheese and mix until the noodles are evenly coated. Add another 1/2 cup of the parmesan and salt and pepper to taste; toss again. Sprinkle with remaining cheese atop and sprinkle with nutmeg just prior to serving.