Pour 1½ cups vegetable juice into about 12 compartments of standard ice cube tray. Freeze until juice is solid.
Add frozen juice cubes, remaining 1½ cups vegetable juice, and all remaining ingredients to FourSide jar in order listed. Secure lid and select "Ice Crush." Pour into chilled glasses, and garnish with black pepper, green olives, and celery sticks.
For a nonalcoholic version, replace the vodka with additional vegetable juice.