In a large saucepan, melt the butter. Add flour and stir well. Cook and stir until the sauce turns the color of coffee with cream.
Add the broth in small amounts, and be prepared for it to bubble up after the first few additions. Stir well between additions to avoid lumps.
After all of the broth has been stirred in (I usually use 1 1/2 cups), add meatballs and cook until meatballs are warmed through. Remove the meatballs from the heat and stir in sour cream. Serve immediately with noodles.