Shred potatoes using a box grater or the shred attachment of food processor. Mix potatoes with potato starch in a medium bowl and add 1 teaspoon salt and 1/2 teaspoon black pepper and stir to combine.
Heat oil in a large non-stick skillet and add potato mixture, pressing down to fill the bottom of the pan in a thin layer, about ½-inch thick. Cook, undisturbed, until the bottom is crispy, about 10 minutes. Transfer to a platter and flip back into the pan; or, if willing, flip directly in the pan. Cook until brown on both sides, another 3-5 minutes.
Transfer potato next to a glass bowl and cover with a similar size bowl to create a next shape. Let cool to set, about 10 minutes. Season with 1 teaspoon salt.
Bring 1 quart water in a medium sauce pan to a boil over high heat and season with 2 teaspoons salt. Cook 1/2 cup peas until tender, about 3 minutes; reserve 1/3 cup cooking liquid. Drain and place in a bowl of ice water to fully cool. Drain peas and add to blender. Add butter and puree, adding reserved cooking water, 1 tablespoon at a time, until smooth. Season with ¼ teaspoon salt. Mix puree, the yolks from 4 egg halves, and 1 Tablespoon mayonnaise and stir until well blended. Pipe mixture into 4 empty egg white halves.
Place beets and horseradish in a blender and mix until smooth, about 30 seconds. Season with 1/8 teaspoon salt. Mix puree, the yolks from 4 egg halves, and 1 Tablespoon mayonnaise, and stir until well blended. Pipe mixture into 4 empty egg white halves.
Mix together yolks from 4 egg halves, 1 tablespoon mayonnaise, and 1/8 teaspoon salt and mix until well blended. Pipe into 4 empty egg white halves. Reserve all deviled eggs in refrigerator until ready to serve.
To assemble the salad, place the potato nest on a platter and add salad greens. Garnish with carrots, peas, radishes, and asparagus. Drizzle on lemon juice and 2 tablespoons olive oil and season with 1/4 teaspoon salt and 1/4 teaspoon pepper. Place deviled eggs throughout the next and garnish with edible flowers, sprouts, and micro greens, if using.