Preheat oven to 300 degrees F.
For the salmon: Place the salmon on a large baking sheet skin-side down. Drizzle salmon with olive oil and season with salt and pepper, to taste. Place into the oven and bake for 30 minutes until flaky. Transfer to a cutting board.
For the Hash: Heat a large saute pan over medium-high heat and add olive oil. Once heated add the potatoes and shallow-fry for about 8 minutes until evenly browned on all sides. Remove the potatoes with a slotted spoon and place onto a paper towel-lined plate. Season with salt and pepper and transfer to a large bowl.
Using 2 forks, flake the salmon, removing it in chunks from the skin, and fold into the potatoes.
Remove most of the oil, leaving only a couple of tablespoons. Place over medium heat and add the sliced onions, sliced peppers and garlic and allow to caramelize. Add the green onions, thyme leaves, paprika and cayenne pepper. Season with salt and freshly ground black pepper, to taste, and stir to combine. Add the potatoes back to the pan and stir to combine.
For the eggs: Place a large saute pan with high sides over medium heat and fill with a few inches of water. Heat until just below a simmer. Add a splash of white vinegar and using a wooden spoon, stir the water in 1 direction to create a small whirlpool. Crack the eggs and add, 1 at a time, to the spinning water. Allow to poach until desired doneness. Remove with a slotted spoon to a plate.
For the hollandaise: Put the egg yolks, lemon zest, lemon juice, mustard, water, salt and pepper, to taste, into a blender. Blend together and then slowly start pouring in the melted butter with the blender running. Stop the blender when all the butter has been incorporated. Taste and adjust the seasoning, if necessary. Thin the hollandaise with a little water, if it is too thick.
Place the salmon-potato hash on serving plates or serving platter and top with the eggs. Pour hollandaise sauce over the eggs and garnish with or dill. Season with salt and pepper, to taste.
Consumption of raw or undercooked eggs, shellfish and meat may increase the risk of foodborne illness.