Ingredients

• 1/2 cup loosely packed flat-leaf parsley leaves
• 1 celery stalk, coarsely chopped
• 1 small shallot, coarsely chopped
• 1 garlic clove, peeled
• 1 cup mayonnaise
• 2 tablespoons whole grain mustard
• 1 tablespoon prepared horseradish
• 1 tablespoon fresh lemon juice
• 1/2 teaspoon paprika
• 1/2 teaspoon Worcestershire sauce
• 1 onion, quartered
• 4 sprigs thyme
• 2 bay leaves
• 1 tablespoon kosher salt plus more
• 1 teaspoon yellow mustard seeds
• 1 teaspoon whole black peppercorns plus freshly ground black pepper
• 2 celery stalks, 1 coarsely chopped, 1 thinly sliced on the diagonal
• 2 pounds uncooked unpeeled large shrimp
• 1 14-ounce can hearts of palm, drained, sliced on the diagonal
• Butter lettuce leaves
• Lemon wedges

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Instructions

1. Pulse the first four ingredients in a food processor until finely chopped. Add mayonnaise, mustard, horseradish, lemon juice, paprika, and Worcestershire sauce; process until smooth. DO AHEAD: Can be made 3 days ahead. Cover and chill.
2. For shrimp: Combine the first 5 ingredients, peppercorns, chopped celery stalk, and 4 quarts (16 cups) water in a large heavy pot. Bring to a boil. Add shrimp and simmer for 3 minutes. Remove pot from heat and steep shrimp until just cooked through, about 5 minutes. Transfer shrimp to a rimmed baking sheet; let cool. Peel and devein shrimp. DO AHEAD: Can be made 1 day ahead. Cover; chill. Toss shrimp and rémoulade in a large bowl to coat. Cover and chill at least 2 hours. Fold hearts of palm and sliced celery into shrimp. Season with salt and pepper. Serve on lettuce leaves with lemon wedges.
3. Combine the first 5 ingredients, peppercorns, chopped celery stalk, and 4 quarts (16 cups) water in a large heavy pot. Bring to a boil. Add shrimp and simmer for 3 minutes. Remove pot from heat and steep shrimp until just cooked through, about 5 minutes. Transfer shrimp to a rimmed baking sheet; let cool. Peel and devein shrimp. DO AHEAD: Can be made 1 day ahead. Cover; chill.
4. Toss shrimp and rémoulade in a large bowl to coat. Cover and chill at least 2 hours.
5. Fold hearts of palm and sliced celery into shrimp. Season with salt and pepper. Serve on lettuce leaves with lemon wedges.