Combine Ground beef, salt and pepper in large bowl, mixing lightly but thoroughly. Lightly shape into eight thin mini-patties. Heat large nonstick skillet over medium heat until hot. Add patties; cook 5 to 6 minutes or until instant-read thermometer inserted horizontally into center registers 160°F, turning once. Top each burger with half cheese slice. Remove burgers; keep warm.
Add onions and mushrooms to same skillet and cook for 2 to 4 minutes until tender. Add eggs and cook and stir 2 minutes until desired doneness. Season as desired.
Place burgers on bottoms of buns. Top burgers evenly with egg mixture. Close sandwiches.
Nutrition information per serving: 254 Calories; 99 kcal Calories from fat; 11 g Total Fat; 4 g Saturated Fat; 3 g Monounsaturated Fat; 98 mg Cholesterol; 556 mg Sodium; 19 g Total Carbohydrate; 1 g Dietary Fiber; 21 g Protein; 1.5 mg Iron; 4.3 mg Niacin; 0.2 mg Vitamin B6; 1.4 mcg Vitamin B12; 3.3 mg Zinc; 16.3 mcg Selenium; 79.2 mg Choline;