To make hollandaise sauce, in a heat-proof bowl, combine egg yolks, butter, milk, and lemon juice and cook on a double-boiler while constantly whisking until the sauce thickens, about 8 minutes. Add in the salt and cayenne pepper and mix well. Set aside.
To make hashbrowns, peel off skin from potatoes and grate the potatoes. Place the grated potatoes in a bowl and let them soak in cold water for about 5 minutes. Drain off water and dry the potatoes using kitchen towel. In a mixing bowl, combine the grated potatoes, all-purpose flour, egg whites, and salt and pepper. Fill a pan with about 1 cm of oil heat on medium heat. Once oil is hot, spoon half of the grated potatoes and gently drop into the hot oil, forming a circular disk shape using the back of the spoon. Do the same with the other half of the potatoes. Fry over medium heat for 5-6 minutes on each side, or until golden brown. Remove from oil and set aside.
To make poached eggs, boil about 2 inches of water in a saucepan. Add salt and vinegar. Lower heat and bring water to a gentle simmer. Crack an egg into a small bowl. Create a whirlpool in the middle of the water in the saucepan by stirring it using a spoon. Quickly and gently transfer the egg from the bowl into the saucepan, placing the egg in the middle of the whirlpool. Let egg cook for about 3 minutes for a runny yolk. Using a slotted spoon, gently remove egg from water and place on a plate. Repeat steps with other egg.
To assemble the dish, place the hashbrowns on a plate. Place the avocado strips on top of the hashbrowns, followed by the red onions. Place a poached egg onto each hashbrown, and pour the hollandaise sauce over it. If hollandaise becomes too thick, add a little bit of hot water and stir. Top with cayenne pepper.