Pull the stems out of mushrooms and scoop out mushroom gills without tearing the caps, set gills aside. In a skillet, saute mushroom caps in olive oil until brown. In a microwavable bowl, beat eggs and milk; mix in bacon and mushroom gills. Microwave egg mixture for 2 minutes; or until there's no visible liquid, stirring every 30 seconds.
Stuff the egg mixture into the cap of the mushrooms. Sprinkle cheese over the eggs. Heat in microwave until cheese is melted.