In a large bowl, combine 1/3 cup bread crumbs, onion, Worcestershire sauce, steak sauce, garlic and seasonings. Add turkey; mix lightly but thoroughly. Shape into four 1/2-in.-thick oval patties. Place remaining bread crumbs in a shallow bowl. Press patties into crumbs, patting to help coating adhere.
In a large nonstick skillet, heat 1-1/2 teaspoons oil over medium heat. Add patties; cook 3-4 minutes on each side or until a thermometer reads 165°. Remove from pan.
In same pan, heat 2 tablespoons oil over medium heat. Stir in flour until smooth; gradually whisk in broth, Worcestershire sauce and steak sauce. Bring to a boil, stirring constantly; cook and stir 1-2 minutes or until thickened. Stir in mushrooms. Return patties to pan. Reduce heat; simmer, covered, 2-3 minutes or until heated through.