• In a food processor, combine the mayonnaise, mustard, tomato paste, horseradish, capers, lemon juice, and paprika. Pulse to mix. With the processor running, slowly add the oil in a steady stream. Add the scallions and parsley; pulse briefly to combine. Chill.
• In a 6- to 8-qt. pan, combine 1 gallon water with 1/4 cup of the salt, the cayenne, peppercorns, lemon quarters, garlic, and onion. Bring to a boil and then simmer for 15 minutes. Add the shrimp and cook until they’re pink and just barely opaque through the center, about 3 minutes. Remove the shrimp and place in a large bowl. Cover with ice. Add the remaining salt. When the shrimp are well chilled, drain.
• Serve the shrimp with the rèmoulade sauce and lemon.

Tip: The shrimp’s fresh, briny flavor meet a delicious topping in this Cajun-inspired starter.