Process the ham in a food processor until finely chopped but not pasty, about 6 or 7 pulses. You may need to do this in batches. Place the finely chopped ham in a large bowl and continue processing the remaining ham.
Add the mayonnaise, onions, relish, and mustard to the processed ham. Mix well and, if the mixture is too dry, add more mayonnaise. Refrigerate until serving. The dried onions absorb some of the moisture from the mayonnaise and relish so you may need to add more mayonnaise before serving.
