In a medium skillet over medium heat, add the butter. When it is melted, add the onions and cook until they begin to soften, about 5 minutes. Add the hot dogs and cook to heat them through.
Whisk the eggs and season with salt and pepper. Lower the heat in the skillet, pour in the eggs, and sprinkle the cheese on top. Cook, stirring often, until the eggs are cooked to your liking. Serve hot.