Pour white wine into pan and scrape up and dissolve any small bits of browned food; stir onion and garlic into white wine. Cook until onion is translucent, stirring often, about 5 minutes. Return browned beef to pan. Stir ketchup, Worcestershire sauce, and juice from canned mushrooms with beef mixture. Reduce heat to low, cover pan, and simmer until beef is tender, about 3 hours.