In a medium skillet, combine 2 tablespoons butter, diced potatoes and onions, and the cubed ham. Cook on medium/high heat, stirring often, for about 10 minutes.
Heat a small skilet on low heat. Add 1/2 tablespoon of butter and melt.
In a bowl, scramble one egg and season with salt and pepper. Pour the mixture into the small, heated skillet.
Allow the mix to sit for a few minutes and then scramble and cook to the desired texture.
Spoon the ham/potato mixture, followed by the eggs, into the tortillas and sprinkle with cheese.
Allow the cheese to melt before serving.
