In a large bowl, whisk together mayonnaise, vinegar, and horseradish. Fold in cornichon, shallot, celery, scallions, and capers. 

Add sliced eggs and just turn the mixture with your hands. Stirring will break up the eggs. I like to get in there with my hands and fold the ingredients very gently together. 

Adjust seasoning with salt and pepper and chopped flat leaf parsley.

Spoon egg salad in lettuce cups or endive leaves before serving.