Cut the deli ham into 1-inch chunks.

Place the ham in a food processor and pulse until coarsely chopped, stopping before it becomes a paste.

Rinse celery stalks under cold water, pat dry, and finely dice them.

Transfer the processed ham to a mixing bowl and add mayonnaise, Dijon mustard, garlic powder, and black pepper; stir until smooth and cohesive.

Fold the diced celery into the ham mixture to distribute evenly.

Stir in the sweet pickle relish until fully incorporated, tasting and adjusting relish or mayo as needed.

Cover and refrigerate the ham salad for at least 30 minutes to allow flavors to meld and to firm up for spreading.

Slice your bread and, if desired, lightly toast it to prevent sogginess.

Spread 3 to 4 tablespoons of chilled ham salad onto each bread slice, top with lettuce leaves or tomato slices if using, and close sandwiches; cut diagonally before serving.