In a small bowl, combine the vinegar, salt and shallot. Stir and let marinate for 5 minutes, then stir in the honey.
Dice the beet and pear and add them to the bowl. The filling can be made up to this point and refrigerated for 4-6 hours.
Separate the leaves from the endive. Spoon a scant tablespoon of filling into each one, then top with the blue cheese crumbles. Lay on a platter and serve, or refrigerate up to an hour.