In a large (12 inch) skillet over medium-high heat, melt the butter. Add the onion and cook the onion until softened, about 4 to 5 minutes, stirring as needed to avoid burning.
To the skillet, add the remaining ingredients. Cook, stirring often until heated through.
If desired, create 6 pockets in the hash and crack one egg into each hole. Cover the skillet and reduce the heat to medium. Cook until the eggs reach your desired doneness. Season the eggs with salt and black pepper prior to serving.