For the corned beef: Mix together the kosher salt, brown sugar and pink salt. Cover both sides of the brisket with the salt cure and refrigerate for a minimum of 10 days.
Rinse off the cure and pat the brisket dry. Place the brisket in a large pot, add water to cover and simmer for 3 hours.
For the hollandaise: Whisk together the egg yolks and lemon juice in a bowl. Set the bowl over a pot of simmering water. Cook, whisking continuously, until the mixture has thickened enough to hold a number eight drawn in the base of the bowl with a whisk. (Don't let the eggs get too hot or they'll scramble.)
Remove the bowl from the pot and, whisking, slowly drizzle in the clarified butter. Continue whisking until the sauce has thickened and doubled in volume. Add the hot sauce and salt. Cover and set aside.
For the poached eggs: Fill a high-sided skillet with five parts water to one part vinegar and bring to a bare simmer. Slide in the eggs, one at a time, and poach until the whites are just set but the yolks are still soft, 2 to 3 minutes. Remove the eggs with a slotted spoon and set aside.
For the corned beef hash: Melt the butter in a saute pan over medium heat. Add the green bell peppers and red onions and saute until the peppers are soft. Add the beef stock and 4 ounces of chopped corned beef to the pan and cook until warmed through.
Meanwhile, in a separate pan, fry the potatoes in the vegetable oil. When crispy, add the potatoes to the corned beef and vegetables and toss to combine.
To assemble: Toast the bagel halves and transfer to a plate, face up. Spoon the corned beef hash over the bagel halves, trying to get as much hash inside the scooped out sections as possible. Top each bagel half with a poached egg and a spoonful of hollandaise sauce.
This recipe was provided by a chef, restaurant or culinary professional. It has not been tested for home use.