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 (spot prawns cook very quickly). 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.
Whisk mayonnaise with 1 tbsp. oil in a small bowl and set aside.
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. "Otherwise, the vinegar will break down the texture of the prawns and they'll get rubbery," says Clark.
Divide salad among plates and spoon a dollop of mayonnaise next to each salad. Sprinkle with black and white sesame seeds and a few drops of oil.
*Most spot prawns are frozen at sea, sold as tails only, and are high quality (a few markets sell live prawns also). Even frozen, spot prawns can be hard to find inland, but can be ordered in season from vitalchoice.com and marxfoods.com. Defrost in the refrigerator, set in a colander over a bowl, up to 2 days before using.
Note: Nutritional analysis is per first-course serving.