1. Combine the 2/3 cup flour, 1/2 teaspoon salt, the paprika and 1/4 teaspoon black pepper in shallow plate. Beat eggs slightly in second shallow plate.
2. Coat beef steaks in flour mixture, shaking off the excess; dip into egg, then back into flour mixture, coating both sides. Refrigerate coated beef on wire rack set over a sheet pan for 20 minutes.
3. Heat oil in large nonstick skillet over medium heat. Add beef, working in batches, if necessary; cook 2 minutes on each side or until cooked through. Transfer beef to platter; keep warm.
4. Pour off all but 3 tablespoons fat from skillet. Stir remaining tablespoon flour into hot fat in skillet until flour forms a paste, about 20 seconds. Stir in milk, mushrooms and Worcestershire. Bring to boiling; lower heat to medium; cook 2 to 3 minutes or until thickened. Season with remaining salt and pepper.
5. Spoon sauce over beef. Garnish with parsley, if desired. Serve hot.