Stir together cucumbers, half the yogurt, 3/4 cup broth, the pieces of scallions, and 1 teaspoon salt; season with pepper. Heat oil in a large skillet over medium heat until hot but not smoking. Add garlic; cook until just golden, about 1 minute. Add spinach; cook, stirring, until wilted, about 3 minutes. Stir into yogurt mixture.

Working in batches, puree mixture in a food processor. Transfer to a large bowl, and stir in remaining yogurt, the onion, and lemon juice. Refrigerate, covered, until cold, about 1 hour.

Meanwhile, put remaining cup broth, 3/4 cup water, and 1/2 teaspoon salt in a medium saucepan; season with pepper. Bring to a boil. Add the shrimp; cook until pink and cooked through, 2 to 3 minutes. Drain. Refrigerate the shrimp, covered, until cold, about 1 hour. Divide the soup and shrimp among 4 bowls. Garnish with julienned scallions.