For the gazpacho, place vinegar, lime juice, yoghurt, salt and 3 tbsp olive oil in a large bowl and whisk together. Add remaining ingredients except the herbs. Toss together until well coated. Cover with plastic wrap and leave in the fridge to marinate for at least 4 hours, ideally overnight.
Place mixture in a blender along with all the herbs. Process on a low setting until ingredients become like a chunky purée. Increase speed to high and gradually add about ½ cup of very cold water to create a smooth mixture. Blend on high speed for a minute then add more water until you achieve a soup-like consistency. Taste and adjust seasoning. Place in the fridge to allow it to become super chilled.
Remove shells from prawns and de-vein. Cut into 1cm pieces. Pour chilled soup into two bowls or glass coupes and top with prawn pieces. Drizzle a tsp of oil on top of each dish. Garnish with paprika and chives, and serve immediately.