Combine ground beef, onion, celery, and garlic in a skillet over medium heat. Cook and stir until beef is browned and crumbly, about 7 minutes. Drain and discard grease, if needed.
Stir cream of mushroom soup, beef broth, mushrooms, and wine into the skillet. Bring to a boil. Reduce heat to low and simmer until stroganoff begins to thicken, 20 to 25 minutes. Add sour cream, salt, and pepper; cook until hot, about 10 minutes.