1. Bring a kettle or medium pot of water to a boil. Arrange prawns in a shallow baking dish in a single layer and sprinkle with 2 tsp. salt. Cover with boiling water, stir once with a spoon, and poach until just barely opaque, 30 to 45 seconds, depending on size If using shrimp, let sit until pink and just opaque, 1 1/2 to 2 minutes. Transfer to ice water to cool, then drain. Continue with recipe; or to make ahead, chill up to 8 hours. One hour or less before serving, peel prawns, and devein if you like.
2. Whisk mayonnaise with 1 tbsp. oil in a small bowl and set aside.
3. Combine cucumber, radishes, arugula, and vinegar in a large bowl; toss to coat. Drain excess vinegar, add prawns and a pinch or two of salt to taste, and toss gently. Serve immediately.
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