If using raw potatoes, start by boiling them until tender. Once cooled, cut the potatoes, meat, apples (if using), and onions into bite-sized cubes.
In a large skillet, melt the butter over medium heat. Add the chopped onions and sauté until they become translucent and fragrant.
Add the diced potatoes to the skillet. Season with salt (and pepper, if desired). Cook, stirring occasionally, until the potatoes develop a golden-brown crust on all sides.
Add the cubed meat to the skillet, mixing well. Allow it to heat through and slightly crisp up, which should take a few minutes.
If you're including apples for a touch of sweetness, add them now. Cook for an additional couple of minutes until the apples soften slightly.
In a separate pan, fry the eggs to your preferred doneness. Traditionally, the yolk is left runny to mingle with the other flavors on the plate.
Plate the Danish Hash, topping each serving with a fried egg. Accompany with pickled beets on the side for a tangy contrast.