Pop stem out of the mushroom cap. Using a spoon, remove the gills of the mushroom.
Place caps in a medium bowl and add olive oil. Toss caps to coat with oil.
Place on a baking sheet and place in the oven for 3-4 minutes.
While the mushrooms are in the oven, start by dicing ham into bite-size pieces.
Using a medium sauté pan, melt butter over medium heat and add ham, peppers, and onions.
Crack eggs and whisk in a medium bowl and then add to the pan. Turn heat to medium-low and allow eggs to cook slowly while pulling eggs away from the side of the pan with a spatula. Continue to cook for 3-5 minutes or until eggs are still soft.
Mix in cheddar cheese and chives and divide and transfer eggs to mushroom caps. Place back in the oven for 3 minutes.