In a large bowl, mix together the egg, milk, bread crumbs, salt and nutmeg. Add beef mince and mix by hand until well blended. Shape into 4 patties. Place a frypan over medium heat. Add patties and brown for 3 to 4 minutes on each side. Remove from the frypan.
Add onion to the frypan and cook until tender but not browned. Drain off excess fat. Whisk together beef stock and flour. Pour into the frypan and stir in Worcestershire sauce and thyme. Cook over medium heat, stirring until thickened. Return patties to the frypan and add green capsicums. Cover and simmer until burgers are cooked through, about 5 minutes.