My mother used to make this too. Sometimes she used to wrap the sandwiches in foil and put the sandwiches in the oven to warm them and melt the cheese which was also very good.
HAM SALAD WITH CHEESE
2 cups diced ham
1 rib celery, cut up
1 onion slice, about 1/4-inch thick
6 to 8 tablespoons mayonnaise
2 tablespoons minced sweet pickles or sweet pickle relish
1 to 2 teaspoons sweet pickle juice, optional
1 hard-cooked egg, diced
1/4 to 1/2 cup Cheese Whiz
6 hamburger buns
In a food processor, combine the ham, celery, onion, and pickles or pickle relish. Pulse until minced; transfer to a bowl. Mix in mayonnaise until well-moistened, along with sweet pickle juice, if using. Mix in Cheese Whiz. Add pepper, to taste, and stir in the diced hard-cooked egg. Spread over hamburger buns. Serves 6.