1. Place each bologna slice in 6-ounce custard cup or coffee mug. Arrange cups in circle on dinner plate. Beat eggs, half-and-half, salt and pepper in 4-cup measure. Mix in mushrooms and green pepper. Microwave uncovered on medium (50%) until hot, 1 to 2 minutes.
2. Stir in shredded cheese. Divide mixture among bologna cups. Cover loosely and microwave on medium (50%) 3 minutes; rotate plate 1/2 turn. Microwave until egg mixture is almost set, 1 to 3 minutes longer. Let stand 5 minutes. (Eggs will continue to cook while standing.)