For an extra hint of sweetness, drizzle the soup with a bit of honey just before serving.
Ingredients
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3 English cucumbers
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½ honeydew melon, peeled, seeded, and cut into 1-inch chunks (8 cups)
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1/2 to 2/3 cup fresh lime juice (from 6 limes), plus wedges for serving
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1 cup lightly packed fresh mint leaves, plus more for serving
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2 cups crushed ice
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Coarse salt
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2 cups Greek yogurt
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Extra-virgin olive oil
Directions
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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.
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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.