Halve eggs lengthwise. Scoop yolks into a mixing bowl and arrange whites on a platter. Mash yolks with finely chopped olives. Add olive brine, salt and white pepper, vodka, Worcestershire, and Tabasco, and combine with just enough mayo to bind.
Transfer egg filling to a plastic food storage bag and trim one corner to make a pastry bag. Fill egg white halves with yolk mixture and garnish with whole blue cheese-stuffed olives on toothpicks. Chill until ready to serve.