Cut the ham into large chunks and pulse in a food processor to mince, taking care not to over-process the meat, or alternatively, chop finely by hand.
Place the minced ham in a medium bowl and add the onion, pickles, pickle juice, celery, mustard, and 1/4 cup of mayonnaise. Mix together.
Taste and add more mayonnaise if desired, then season with cracked black pepper.
Refrigerate until ready to serve.