Prep the vegetables by chopping the celery and scallions, then pulse them with the sweet pickle relish in a food processor until they reach a rice-size texture. Transfer to a mixing bowl.

Chop the deli ham into 1-inch chunks and pulse in the food processor until finely minced, leaving some larger pieces. Combine with the veggie mixture.

In the mixing bowl, add the cream cheese, mayonnaise, yellow mustard, and paprika to the ham and veggie mix. Mix thoroughly until smooth yet chunky. Season with salt and pepper as needed.

Serve the ham salad on soft rolls, bread, or crackers, or enjoy it over a garden salad. Store leftovers in an airtight container in the refrigerator for up to five days.