Whirl cucumbers, garlic, lemon juice, oil, and 1 container yogurt in a blender until smooth. Pour into a stainless steel bowl and whisk in remaining yogurt, 2 tsp. Aleppo pepper, the salt, and black pepper.
Nest bowl in ice water; stir often until cold, about 15 minutes.
Stir chopped mint and dill into soup just before serving. Sprinkle bowls with more Aleppo pepper, if you like, and mint leaves.
*Buy Aleppo pepper from grocery stores or worldspice.com, or buy dried California chiles in Latino markets (pulse in a food processor to grind coarsely).
Note: Nutritional analysis is per 1-cup serving.