Persian Carpet

In a blender, whirl 1 1/2 cups coarsely chopped English cucumber (for best color, leave peel on), 2 cups plain whole-milk yogurt, and 2 teaspoons chopped fresh mint leaves until very smooth. Add kosher or sea salt to taste (1/4 to 1/2 teaspoon). Fill four tall glasses (16-oz. capacity) halfway with ice cubes. Pour yogurt mixture equally into glasses. Slowly fill each glass to the rim with cold seltzer water. Garnish with fresh mint sprigs.