Ingredients
3 English cucumbers
1/2 honeydew melon, peeled, seeded, and cut into 1-inch chunks (8 cups)
1/2 to 2/3 cup fresh lime juice (from 6 limes), plus wedges for serving
1 cup lightly packed fresh mint leaves, plus more for serving
2 cups crushed ice
Coarse salt
2 cups Greek yogurt
Extra-virgin olive oil
Preparation
Peel, halve, and seed 2 cucumbers, then coarsely chop. (You should have about 4 1/2 cups.) Halve and seed remaining (unpeeled) cucumber; cut into a 1/4-inch dice. Working in batches, puree chopped cucumbers, melon, 1/2 cup lime juice, mint, and ice in a food processor or blender. Season with salt and more lime juice. Transfer soup to a bowl, cover, and refrigerate until ready to serve, up to 2 hours.
Smear 1/4 cup yogurt onto two sides of each serving bowl. Spoon chilled soup into bowls, drizzle with oil, and sprinkle with diced cucumbers and mint. Serve, with lime wedges.