Prepare the potatoes. Place the diced potatoes in a saucepan of well-salted cold water. Bring to a simmer and cook for 5–7 minutes, until just beginning to soften. Drain thoroughly and leave to steam-dry.
Cook the home fries. Heat the neutral oil or beef tallow in a large frying pan over medium-high heat. Add the potatoes and cook for 8–10 minutes, turning occasionally, until golden.
Add the diced onion and cook for another 4–5 minutes. Add the butter, paprika, garlic powder, salt and cracked black pepper. Toss until the potatoes are crisp and deeply golden. Finish with parsley and keep warm.
Brown the corned beef. Melt 10 g butter in a frying pan over medium heat. Add the sliced corned beef and cook briefly until the edges turn golden. Reserve a small handful for serving and set the remainder aside.
Start the cream sauce. Melt the remaining 30 g butter in the same pan over medium-low heat. Add the shallot and cook for 3–4 minutes, until soft but not browned.
Stir in the flour and cook for 1–2 minutes. Gradually whisk in the milk until smooth, then add the cream.
Simmer gently for 4–5 minutes, stirring regularly, until the sauce is thick and velvety.
Stir in the Dijon mustard, Worcestershire sauce, white pepper, cracked black pepper and nutmeg. Fold in the corned beef, excluding the reserved crispy pieces, and warm through for 2–3 minutes. Add a splash of milk if the sauce needs loosening.
Taste the sauce and add salt only if needed, as the corned beef will already contribute saltiness.
Prepare the toast. Toast the bread until golden and spread generously with butter.
Cook the eggs. Heat the butter and a small drizzle of oil in a non-stick frying pan over medium heat. Add the eggs and cook until the whites are nearly set. Carefully flip and cook for another 20–30 seconds, leaving the yolks soft. Season with salt and cracked black pepper.
Serve. Spoon the creamed corned beef over the buttered toast. Add the home fries and two over-easy eggs to each plate. Finish with the reserved crispy corned beef, chopped chives or parsley and extra cracked black pepper.
