Process sun-dried tomatoes and 1/3 cup vegetable juice in a processor until tomatoes are finely chopped and mixture is almost smooth. Transfer to a pitcher, and stir in remaining vegetable juice, Clamato, horseradish, fresh lemon juice, Worcestershire sauce, hot sauce, celery salt, and beef base.** Chill thoroughly. Stir in chilled vodka.
*If salt is a concern, use low-sodium vegetable juice and add beef base to taste.
**Beef base is paste-type bouillon concentrate that adds a rich flavor to these drinks. We like Better Than Bouillon brand. Look for organic versions, too.