Line a baking pan with parchment, and bake the cubed sweet potato at 350F for 20 minutes. It is ok if they are still a bit firm, the will cook again with the egg.
Meanwhile prepare the cups.
Place one slice of deli ham in each of the 6 muffin tin cups and set aside until sweet potatoes are done.
In a medium bowl, whisk the egg and milk until combined.
Add the green pepper, mushrooms, and green onions to the egg mixture.
When the sweet potatoes are done, divide them evenly into the ham cups.
Pour the egg mixture on top of the sweet potatos until the muffin tin cups are full.
Sprinkle with cheese.
Bake at 350F for 15-20 minutes - or until the egg is fully cooked.
Let cool completely before putting into a storage container to prevent them from going soggy.