Heat butter or olive oil in a skillet over medium heat then add diced potatoes and cook until they start turning tender and golden, about 10 minutes.
Add the chopped onion and bell pepper to the skillet and continue cooking until the onion becomes translucent and the bell pepper softens, roughly 5 minutes.
Mix in the diced corned beef and stir occasionally as it warms through completely; season with salt and pepper to your liking.
Combine egg yolks, lemon juice, and cayenne pepper in a blender and blend on medium speed until the color lightens, about 20-30 seconds.
With the blender running on low, gradually pour in the melted butter until the hollandaise sauce is creamy and smooth; add salt to taste.
Fill a saucepan with water and bring to a gentle simmer, adding a splash of vinegar to help eggs set.
Carefully crack each egg into a small cup, then gently slide into the simmering water and poach until whites are set but yolks remain runny, about 3-4 minutes; remove with a slotted spoon and drain on paper towels.
Toast the English muffin halves until they’re golden and crisp while eggs are poaching.
Place a generous spoonful of the corned beef hash on each toasted muffin half and top with a poached egg.
Ladle the warm hollandaise sauce over the eggs and finish with chopped chives or parsley if you like.
