Mix flour, salt, and pepper together in a bowl. Pound mixture into the beef. Cut beef into 1/2-inch strips.
Melt butter in a saucepan over medium heat. Add beef; cook until browned, about 10 minutes. Remove meat with a slotted spoon, transfer to a covered container, and refrigerate while you make the gravy; do not wash the pan.
Stir water, onion, and garlic into the pan. Cook and stir over medium heat until all of the brown bits have been scraped from the bottom of the pan, about 5 minutes. Add mushrooms and cream of mushroom soup. Cook until mushrooms are tender, about 20 minutes.
Mix beef and gravy in a pot over medium heat until hot but not boiling, about 5 minutes. Add sour cream and serve.