Preheat oven to 325 degrees.
In a large nonstick skillet, melt butter over medium heat. Add pepper and onion and saute until the onion starts to turn golden brown around the edges. Set aside to cool.
While the vegetables are cooking, line 12 muffin tin cups with 2 slices of ham each. Make sure that any holes in the ham are not aligned, so as to avoid leakage.
In a medium bowl, whisk together the eggs, cream, salt, and pepper. Add the vegetables. Ladle evenly into each muffin cup, being careful to not fill over the edges. Top each one with the cheese.
Put in the oven for 10-15 minutes, until the edges of the ham start to brown and the eggs begin to set. Remove the tins from the oven and tent them with aluminum foil, making sure that the foil does not touch the eggs and that you leave a bit of room for them to expand. You may want to spray the inside of the aluminum foil with cooking spray to make sure they don't stick.
Return them to the oven and cook for another 10 minutes. Remove the foil and bake for 5 minutes more, for a total of 25-30 minutes.
For one serving (2 muffins), macros are 318 calories, 5 grams net carbs, 20 grams protein, and 22 grams of fat.