How to Make It
Fill a large bowl with ice water. In a large saucepan, cover the eggs with water by 1 inch and bring to a boil. Cover and remove the pan from the heat. Let stand for 10 minutes. Drain the eggs and transfer to the ice water bath to cool completely.
Peel and halve the eggs lengthwise. Transfer the yolks to a medium bowl and mash with the back of a spoon. Arrange the egg whites on a platter. Add the mayonnaise, mustard, shallot, 2 tablespoons of chives, the parsley, capers, thyme, vinegar and Tabasco to the bowl with the egg yolks and whisk until smooth. Season with salt. Transfer the mixture to a piping bag and fill the egg whites (or use a small spoon). Top each deviled egg with some of the crab and garnish with caviar and chives.