Mix beef, bread crumbs, egg, onion, garlic, parsley, salt, and pepper together in a bowl. Shape into fifteen 2-inch meatballs. Pour flour into a shallow dish; roll meatballs in flour until coated.
Heat oil in a deep skillet over medium heat. Fry meatballs until browned on all sides and partially cooked through, about 5 minutes. Remove from the skillet and set aside.
Add carrots, onion, mushrooms, and garlic to the same skillet. Cook over medium heat, stirring often, for 10 minutes. Add red wine, broth, garlic and herb seasoning, thyme, salt, pepper, and bay leaf. Return the meatballs to the skillet. Reduce heat to low, cover, and simmer until flavors blend, about 2 hours.