Chef Grant Achatz says of this salad: "I think shellfish benefits from a little sweetness." He suggests draining the fruit in a colander after you cut it, for a cleaner presentation.Plus: More Seafood Recipes and Tips
In a blender, puree the cucumbers with the sugar, rice vinegar and salt. Strain the puree through a fine sieve set over a medium bowl. Refrigerate the cucumber water until chilled.
In a large bowl, toss the red and yellow watermelon with the tomatoes, cucumber, shallots, extra-virgin olive oil, lemon juice and tarragon. Cover and refrigerate for at least 2 hours and for up to 6 hours.
Shortly before serving, light a grill or heat a grill pan. In a large bowl, toss the shrimp with the pure olive oil and season with salt and pepper. Grill the shrimp over high heat until browned and just cooked, about 3 minutes per side.
Spoon the watermelon salad into 4 shallow bowls. Arrange the grilled shrimp on top. Ladle the cucumber water into each bowl, top with the baby salad greens and serve.
The cucumber water can be made up to 1 day ahead. Stir before adding to the salad.