Preheat oven to 375 degrees. Prepare noodles according to package directions, drain.
Meanwhile, in hot butter in a large skillet over medium heat, saute the onion, garlic, and mushrooms. Saute until the onion is golden, about 5 minutes.
Add beef to the skillet. Cook and stir until it is browned about 10 minutes. Remove from the heat. Stir in flour, tomato sauce, tomato paste, beef broth, salt, and pepper.
Return the pan back to the hear and simmer 10 minutes, stirring occasionally. Blend in sour cream.
In a lightly greased 2-quart casserole dish, layer a third of the noodles, then a third of the meat mixture. Repeat twice. Sprinkle with cheese.
Bake uncovered for 25 minutes.