Crack the eggs and separate whites from the yolks, keeping the whites reserved in 4 small bowls or cups containing 2 whites each. (Yolks can be reserved and used for another purpose.)

Heat a 10-inch nonstick skillet or crepe pan over medium heat and brush the pan lightly with olive oil. Add two whites to the pan and swirl to coat the bottom of the pan evenly. Cover the pan and cook until the whites are firm and cooked through, 3 to 4 minutes. Transfer the cooked whites to a plate and cover with a piece of parchment or wax paper. Repeat with the remaining whites. You should have 4 egg white circles. Cover with plastic wrap and refrigerate until thoroughly chilled.

While the whites are chilling, cook the shrimp:  Fill a medium saucepan two-thirds full with water and add the onion quarters and bay leaves. Bring to a boil over medium high heat.

Add 1 quart of cool water to a large bowl along with the 3 tablespoons kosher salt, lemon juice, and crab boil. Stir to dissolve salt. Add 2 quarts of ice and set the seasoned ice bath aside.

When the water comes to a boil, add the shrimp and cook just until the shrimp curl and turn opaque, usually 3 to 4 minutes. Drain the shrimp and promptly transfer them to the ice bath until completely cool. Once cooled, drain the shrimp in a colander and pat them dry. Refrigerate until ready to serve the salads.

When ready to serve, place one egg white circle onto each of 4 salad plates. Add a handful of the arugula to the center of the egg white. Toss the shrimp in enough of the remoulade sauce to coat, and arrange them on top of the arugula. Top with some of the Pickled Red Onions and drizzle with more remoulade sauce if desired.