Preparation Bring medium saucepan of lightly salted water to boil. Add shrimp and cook just until bright pink and opaque in center, about 3 minutes. Drain; rinse under cold water. Peel and devein shrimp; transfer to processor. Add green onions, shallot, and tarragon; using on/off turns, process until shrimp are finely chopped. Transfer shrimp mixture to medium bowl. Mix in mayonnaise and next 3 ingredients. Season to taste with salt and pepper. Cover and chill at least 2 hours. (Can be made 1 day ahead. Keep chilled.)
Preparation Bring medium saucepan of lightly salted water to boil. Add shrimp and cook just until bright pink and opaque in center, about 3 minutes. Drain; rinse under cold water. Peel and devein shrimp; transfer to processor. Add green onions, shallot, and tarragon; using on/off turns, process until shrimp are finely chopped. Transfer shrimp mixture to medium bowl. Mix in mayonnaise and next 3 ingredients. Season to taste with salt and pepper. Cover and chill at least 2 hours. (Can be made 1 day ahead. Keep chilled.)