How to Make It
Make the paprika hollandaise: Place a large bowl over a saucepan containing simmering water. In the bowl, whisk together egg yolks, smoked paprika, Tabasco, and lemon juice. Whisk vigorously to double volume. Slowly whisk in the melted butter to create an emulsion. Adjust seasoning as needed and set aside in a warm place.
Pickle the red onions: In a saucepan, combine the wine vinegar, sugar, and salt. Bring to a boil, stirring to dissolve the sugar. Add the thyme, bay leaf, and red onions and stir to coat evenly. Cook briskly for exactly 1 minute over high heat and remove from the heat. Allow the mixture to stand until it cools to room temperature. Transfer to a sealed container and refrigerate for up to 2 days.
Bake the rösti: Preheat oven to 350°F. Using a box grater, shred the potatoes into a bowl of water. Rinse the excess starch from potatoes, place in a towel and squeeze the excess moisture from potatoes. Place the potatoes in a bowl and toss with butter and salt. Portion the potato mixture into 12 equal size piles and shape into round disks. Heat a non-stick pan over medium heat and add disks. Cook each disk for about 2 to 4 minutes on each side until golden brown. Remove to baking rack on a sheet pan and bake in oven for 15 minutes before.
Assemble the avocado eggs Benedict: Roughly cut avocados and place in bowl. Add the aioli and the shrimp and mix together. Adjust seasoning as needed. Place 2 röstis down on a plate, top with avocado mixture, 2 poached eggs. Cover with hollandaise and pickled onions. Serve.