In a large saucepan, bring 6 cups of water to boil. Add 1 teaspoon salt and shrimp. Boil 3 minutes or until shrimp are pink, then drain shrimp, let cool, peel and devein. Save and refrigerate 4 whole shrimp for garnish and finely chop remaining shrimp. Set aside.
In a large bowl, stir together cucumber, fennel, garlic, onion, dill, buttermilk and chopped shrimp. Adjust seasoning with salt and white pepper. Cover and refrigerate at least 2 hours.
Divide the cold soup among 4 chilled bowls and top each with a whole shrimp.