Make the cheese sauce: Melt the butter in a small pot over medium high heat and whisk in the flour. Whisk in the milk and bring to a simmer. Simmer for about 5 minutes or until it starts to thicken. Stir in the cheese until melted.
Place the torn English muffin or soda bread on a plate. (The reason for the tearing? I don’t like struggling to cut through an English muffin when I eat eggs benedict. If you don’t mind, you don’t have to tear it.)
Put a generous amount of corned beef on top of the muffin. Top with poached egg, and pour the cheese sauce over all. Garnish with parsley and serve at once.