Chop the egg whites and yolks separately and put them in separate bowls.
Add the mayonnaise, relish, mustard, shallots, vinegar, chives and dill to the yolks and whisk until smooth. Whisk the bacon fat into the yolk mixture. Loosen with more vinegar or mayonnaise if necessary. Fold in the chopped egg whites and season with salt and pepper.
Serve with assorted crudite for dipping.