In a blender, whirl 1 cup buttermilk, yogurt, arugula, 1/2 cup chives, parsley, and shallots until almost smooth. Pour into a bowl; stir in remaining buttermilk and the lemon juice. Season to taste with salt and pepper. Cover and chill until cold, at least 1 hour, or up to 1 day.
Reserve about 1/4 cup shrimp; mound remainder equally in four wide, shallow bowls. Pour soup around shrimp; top servings equally with reserved shrimp and more pepper and chives.