Melt butter in a large saucepan over medium heat. Add garlic and onion and saute for 5 minutes. Add goose breast and brown on both sides for about 5 minutes, or until browned.
Place goose breast in slow cooker and add Worcestershire sauce. Add chicken broth to cover (approximately 2 cups) and cook on High setting for 6 to 8 hours, or until meat falls off bone. Shred with a fork and mix with your favorite barbecue sauce.