Bring a large pot of water to a boil. Cook egg noodles in boiling water until done, about 8 minutes. Drain.
Meanwhile, prepare the sauce. In a large skillet, cook mushrooms and onions in 2 tablespoons of butter over medium heat until soft; remove from pan.
Using the same pan, melt remaining butter. Cook ground beef in melted butter until browned. Mix in flour. Stir in beef broth, and cook until slightly thickened. Add mushroom and onion mixture; stir in sour cream. Season to taste with salt and pepper. Continue cooking until sauce is hot, but not boiling. Serve sauce over egg noodles.