How to Make It
In a heatproof medium bowl, whisk 1 tablespoon of the lemon juice with the ketchup, onion, Worcestershire sauce, pickle relish, sugar, salt and cayenne. Place the bowl over a saucepan of just-simmering water and keep warm.
In a blender, combine the remaining 1 tablespoon of lemon juice with the egg yolks and 1/2 tablespoon of water and blend until smooth. With the blender on, slowly drizzle in the melted butter until the sauce is emulsified. Gently fold the hollandaise into the ketchup mixture and keep warm.
Preheat the oven to 425°. Fill a high-sided skillet halfway with water. Add the vinegar and bring to a boil. Reduce the heat to maintain a steady simmer. Crack each egg into a ramekin and add to the water. Poach the eggs until the whites are set and the yolks are runny, about 3 minutes. Using a slotted spoon, gently transfer the eggs to a paper towel–lined plate to drain. Cover the poached eggs with foil to keep warm.
On a baking sheet, toast the rye bread for 8 minutes, turning once. Top with the corned beef and bake for 2 more minutes. Top each toast with sauerkraut, a poached egg and the Reuben hollandaise. Sprinkle with parsley and serve immediately.