Preheat oven to 400 degrees.

Lightly brush muffin cups with oil or spray. This is important even in a nonstick pan because some of the egg inevitably will seep under the ham and may stick.

Line the muffin tin with one piece of ham in each cup. The ham will stick up a bit and form a cup shape. It’s easiest to “fold in” the opposite ends of the ham and then push back against the tin. Drop about a tablespoon of shredded cheese in the ham cup. If you put more cheese then you should use medium size eggs instead of large, otherwise the egg will spill over the ham edges.

Optional: Crack an egg and pass it between the two egg shells so that the egg white falls into one of the ham cups and the yolk can gently be placed in a bowl.  Repeat putting all of the egg yolks into one bowl.  

Sprinkle with kosher salt and pepper.

This step is so that the egg white cooks through and the egg yolk stays a little runny.  If that's not important to you then go ahead and crack the whole egg directly into the ham cups.

Pop the muffin tin into the oven and cook for 8 minutes (if you cracked the egg whites and yolk all at once then cook for 15 minutes).  Remove from the oven and gently place an egg yolk with a spoon into the ham cups.  Cook for another 8 minutes.

The goal is to keep whole yolks for appearance sake, but don't fret if a yolk breaks. It's pretty in a different way.

Bake until the whites are cooked and the yolks set. 15 total minutes is perfect for a slightly runny yolk. If you want the yolk cooked through, then bake 3 more minutes.

Remove ham cups with a rubber spatula in one hand and pull the ham with the other hand, gently remove and place on serving platter. Top with sliced green or red onions, or both.