1. Heat 2 teaspoons of the oil in a large (PFOA-free) nonstick skillet over medium. Add the mushroom caps, rounded side up, and cook for 5 minutes.

2. Flip over the mushroom caps, sprinkle with the salt and pepper, and top both caps with the cheese and one cap with the ham. Cook the topped mushrooms until well done, about 5 minutes more.

3. Meanwhile, heat the remaining 1 teaspoon oil in a small (PFOA-free) nonstick or cast iron skillet over medium. Add the egg and fry until desired doneness, about 4 minutes.

4. Transfer the ham topped mushroom cap to a plate, top with the egg, and place the remaining mushroom cap on top, cheese side down.