Melt the butter in a large skillet, preferably cast iron, over medium heat. Add the onion and cook for several minutes, until translucent.

Add the chopped corned beef and potatoes. Spread the mixture evenly across the skillet.

Increase the heat to medium-high and press the mixture firmly into the skillet with a metal spatula. Let it cook without stirring until the bottom is nicely browned and crispy. You should hear it sizzling—that's a good thing.

Use the spatula to peek underneath and check the browning. Once the mixture is well browned, flip it in sections and press it down again. Continue cooking until the second side is also nicely browned.

If the mixture begins sticking excessively, add a little more butter to the skillet. Continue cooking until the corned beef and potatoes are crisp and golden.

Remove from the heat and stir in the chopped parsley. Season generously with freshly ground black pepper and add salt to taste.

Serve hot with fried or poached eggs for a hearty breakfast.