Cut the celery in large dice, including the leaves, and puree in the bowl of a food processor fitted with the steel blade. Add the horseradish, shallot, Worcestershire sauce, celery salt, kosher salt, Tabasco and lime juice and process until smooth. Pour the mixture into a large pitcher, add the tomato juice, and stir.
Pour into tall glasses and serve each with the top half of a celery stalk.
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