Step 1

Make the shrimp: Prepare an ice-water bath. Bring a large pot of generously salted water to a boil. Boil shrimp until opaque, 3 to 4 minutes. Drain, and transfer to ice-water bath to cool. Drain, and refrigerate.

Step 2

Make the mango-basil sauce: Pulse mangoes, lemon rind and juice, vinegar, salt, and white pepper in a food processor until smooth. Fold in basil. (Sauce can be refrigerated for up to 1 day.)

Step 3

Make the tomato-horseradish sauce: Stir together chili sauce, horseradish, and lemon juice. Season with black pepper. (Sauce can be refrigerated for up to 1 week.)

Step 4

Make the remoulade: Whisk together mayonnaise, ketchup, and mustard. Stir in celery, parsley, and scallion. Season with black pepper. Serve immediately (or refrigerate for up to 1 day).

Step 5

Place shell-on shrimp in a large bowl, or peel shrimp and arrange in small serving dishes. Serve with the 3 sauces on the side.