How to Make It
Combine all of the remoulade ingredients in a medium bowl and stir well.
In a large pot, combine all of the ingredients except the shrimp and arugula and bring to a boil. Cover and simmer the shrimp over moderate heat for 5 minutes. Uncover, add the shrimp and bring back to a simmer. Cover, remove the pot from the heat and let stand until the shrimp are just cooked through, about 10 minutes.
With a slotted spoon, transfer the cooked shrimp to a large rimmed baking sheet and let cool to room temperature. Cover with plastic wrap and refrigerate the shrimp until chilled.
Peel the shrimp. Line a platter with the arugula and top with the shrimp. Serve with the remoulade sauce.