Toss vinegar, salt, and water together in a large shallow dish. Place radish in the liquid and turn to coat. Let sit in mixture covered in the fridge for 1 hour.
Make the filling by blending all ingredients in an immersion blender until smooth. Too thick? Add some water. Should be a hummus consistency. Taste and adjust seasoning with salt/vinegar.
Take radish out of the fridge and assemble on serving plate.
Match each piece of radish with a pair that is similar in size.
Place a dime-sized piece of filling in the center of the radish. Using wet fingers, place the other on top and pinch the edges shut. Place on plate. Continue until finished.
Sprinkle with water/vinegar mixture and chopped dill. Enjoy!