Combine 3 tablespoons milk and egg whites in a shallow dish, stirring with a whisk. Combine 1/3 cup flour and next 4 ingredients (1/3 cup flour through pepper) in a shallow dish. Working with 1 steak at a time, dip in egg mixture then dredge in flour mixture. Repeat procedure with remaining steaks.
Heat oil in a large nonstick skillet over medium-high heat. Add steaks and cook 3 minutes on each side or until browned. Remove steaks from pan and keep warm.
Add mushrooms to pan and sauté 3 minutes. Combine 2 1/2 tablespoons flour, 1/4 teaspoon salt, and broth, stirring with a whisk. Add broth mixture to pan. Bring to a boil and cook 1 minute, stirring constantly. Spoon over steaks.