Step 1

Soak cured lemons briefly in a bowl with cold water to remove curing brine, about 10 minutes. Dry lemons with paper towels and finely mince.

Step 2

Stir minced lemon, mayonnaise, tarragon, and lemon juice together in a bowl. Cover bowl with plastic wrap and chill aioli in the refrigerator until cold, at least 15 minutes.

Step 3

Preheat an outdoor grill for high heat, and lightly oil the grate.

Step 4

Put shrimp in a bowl. Drizzle olive oil and sprinkle paprika and salt over the shrimp, stir to coat shrimp completely.

Step 5

Cook the shrimp on the preheated grill until they are bright pink on the outside and the meat is no longer transparent in the center, about 2 minutes per side. Transfer shrimp to a plate and serve with lemon aioli.