Melt 2 tablespoons butter on a large cast-iron griddle over medium-high heat and cook the onion for 5 minutes until soft.
Add the potatoes, corned beef, salt and pepper, mix once and press the hash into an even layer.
Cook undisturbed for 6 minutes until the underside forms a deep brown crust, turn the hash in broad sections and cook for 5 minutes more.
Melt the remaining butter in a separate skillet and fry the eggs until the whites are set and the yolks remain soft, or to your preferred doneness.
Divide the crisp hash among 4 plates and set one fried egg on each serving.