Combine first 6 ingredients in a large mixing bowl; mix well. Shape mixture into 6 patties.
Dip each patty in beaten egg; dredge in flour. Fry patties in hot oil in a large skillet until golden brown, turning once. Drain on paper towels. Transfer patties to a serving platter, and keep warm.
Drain off pan drippings, reserving 2 tablespoons in skillet. Stir in 1 tablespoon flour; cook over medium heat, scraping sides of skillet with a wooden spoon to loosen browned crumbs. Gradually add milk, stirring constantly, until thickened and bubbly. Serve gravy with steaks.