HOLLANDAISE SAUCE: In a blender or food processor, put the egg yolks, mustard, cayenne, and water. Blend this together and then slowly start pouring in the warm butter with the blender running to incorporate. Add the lemon juice, salt, and pepper. Thin with a little water if it's too thick. Keep warm.
HASH: Heat the oil in a nonstick skillet over medium heat. Add the potatoes, and carrots. Cook until soft, about 10 minutes. Add the onion, corned beef, and chives, and cook 5-10 minutes, turning occasionally. If desired for crispiness, during the last few minutes, don't turn the hash in order to create a searing or browning on the bottom.
EGGS: ln a large skillet filled with 2" of water, bring it to a boil, and add the vinegar. Reduce the heat to a simmer and crack the eggs carefully into the water. Using a spoon, spoon water up over the top of the eggs several times while they cook. Simmer until the eggs are set, about 3-4 minutes. Remove the eggs with a slotted spoon and place them on paper towels to dry them off.
SERVE: Place the hash evenly onto warm serving plates. Using the back of a spoon, make a hollow in the center of the hash. Place a poached egg into the hollows and then top with hollandaise; garnish with chives.