Shell eggs, then cut in half lengthwise. Transfer yolks to small bowl and mash with fork. Mix in oil, mayonnaise, and mustard. Stir in minced celery, tarragon, capers, and shallot. Season to taste with salt and pepper.
Spoon yolk mixture into whites. Garnish each with celery slice. (Can be made 4 hours ahead. Cover loosely and refrigerate.)
