Bring a medium pot of salted water to a boil. Add potato and cook until tender but still firm, about 15 minutes. Drain, cool, peel and slice.
Preheat oven to 350 degrees. Beat together eggs, salt, pepper and parsley.
In a cast iron skillet, heat olive oil over medium-high heat. Sauté onion and red pepper until soft, and then stir in mushrooms. When mushrooms start to shrink, add the chopped ham, potato and tomato slices. Pour in the egg mixture; gently stir to combine.
Sprinkle cheese on top of eggs and place skillet in preheated oven. Bake until eggs are firm, about 10 to 15 minutes. Allow cooling briefly before serving.