Instructions: Combine first 4 ingredients in large saucepan; boil 10 minutes. Add shrimp; cook just until opaque in center, about 1 minute. Drain. Transfer shrimp to bowl. (Can be made 1 day ahead. Cover; chill.)

Peel cucumbers and cut lengthwise in half. Using spoon, scrape out seeds and discard. Coarsely grate cucumbers. Transfer cucumbers to bowl of ice water. Whisk oil, vinegar, shallots, dill, and sugar in medium bowl; season with salt and pepper. (Cucumbers and vinaigrette can be made 3 hours ahead. Cover; chill.)

Drain cucumbers well. Transfer to paper towels; pat dry. Return cucumbers to bowl. Add 1/4 cup vinaigrette to bowl with shrimp and toss. Add remaining vinaigrette to cucumbers; toss to coat. Arrange 1 lettuce leaf on each of 8 plates. Using slotted spoon, divide cucumbers among lettuce leaves. Top each serving with 3 shrimp.

This recipe yields 8 servings.

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