Cut rolls in half. Mix the Dijon mustard with the honey and spread the bottom of each roll with some of the honey-mustard mixture.
Layer each sandwich as follows: Fold a few pieces of ham and place it on top of the honey-mustard. Top the ham with a pineapple ring, cut in half, if desired. Top pineapple with a slice of cheddar cheese, and the top half of the roll.
Wrap each sandwich well with heavy-duty aluminum foil. Place the sandwiches over hot coals or a grill rack until hot, about 20 minutes depending upon the temperature of your fire. Alternatively, you can bake these sandwiches directly on top of the center rack in a 400 degree Fahrenheit oven for 15 minutes. Carefully unwrap and enjoy!