Pour tomato juice into a pitcher.
Muddle the horseradish, celery salt, balsamic vinegar and pepper at the bottom of a sealable pitcher or container. Add basil and muddle again. Add the remaining ingredients, shake well and strain into the pitcher to serve.
To serve, pour 1 1/2 ounces of vodka into an ice-filled rocks glass. Fill with tomato mixture, stir gently and garnish with a fresh basil sprig and a bocconcini on a spear and a fresh crab claw.
Make a pitcher of this mix ahead of time and you can add the vodka by the glass when you serve.