Place the corned beef in a medium-sized skillet over medium heat. Flip the slices of corned beef and cover them with 1 slice of Swiss cheese. Move the corned beef to the side of the skillet.
Add about a teaspoon of butter to the skillet and cook the egg in the melted butter. If your skillet is nonstick, you can skip the butter if you prefer. Season with salt and pepper.
Spread honey mustard onto the toasted English muffin. Place the corned beef with Swiss cheese on the bottom half of the muffin, followed by the egg. Top with the remaining slice of Swiss cheese and cover with the other half of the English muffin.