Add the noodles to 4 quarts of cold water in a 6-quart pot, cover and place over high heat. Cook to al dente, 18 to 22 minutes, stirring occasionally.
Melt the butter in a 12-inch straight-sided saute pan set over medium-high heat. Increase the heat to high, add the mushrooms and sprinkle with salt. Saute until they darken in color, soften and give off their liquid, 5 to 6 minutes. Add the white bottoms of the green onions and saute 2 to 3 minutes.
Sprinkle in the flour and stir to combine. Cook until the flour disappears and the fond on the bottom of the pan turns dark brown, about 1 minute. Deglaze with the beef broth. Bring to a simmer and decrease the heat to medium-low. Cook for 10 to 12 minutes, and then add the sour cream, goat cheese and black pepper. Stir to combine, and then partially cover and bring to a simmer to warm through, 2 to 4 minutes.
Drain the noodles, add to the pan and stir to combine. Garnish with the green onion tops and additional black pepper. Serve immediately.
Recipe courtesy of Alton Brown, 2012