At your next family dinner, serve shrimp cocktail with not one but three easy, crowd-pleasing dipping sauces—mango-basil, remoulade, and tomato-horseradish.
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.
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.)
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.)
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).
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.