Preheat your grill to medium high heat and make sure to leave a "cold spot" (a section of the grill without direct heat) where you'll be able to cook the apples.
You can accomplish this by leaving one side of a gas grill turned off while turning the other onto high heat.
For a charcoal grill, simply move the coals to one side before lighting them.
Wash and dry the apples before cutting them into round slices about 3/4 inches thick.
Remove the seeds and stem pieces.
Brush liberally with melted butter on all sides.
Do not peel the apples, as they'll likely fall apart while on the grill if you do.
You can, however, core the apples if you feel like it.
Though optional, you might find it helpful to push the apple slices through bamboo skewers to give you more control during cooking and to enhance the presentation before serving.
Place your apple slices off direct heat into the cold spot established during preheating.
If you fear they might fall apart during cooking, place them inside of a grill basket instead of directly on the grates so any stray pieces can be collected at the end.
Leave them to grill for approximately 6 minutes before turning and cooking for an additional 6 minutes on the other side.
By the time the apples are fully done, there should be thick grill marks on both sides.
When the apples are fully cooked, remove them to a plate or bowl to cool.
The apples will be extremely hot when they first leave the heat, so be careful when handling them so you don't hurt yourself.
As soon as they have been taken off the grill, sprinkle with cinnamon and cover with honey.
You're encouraged to use more honey than the recipe calls for if you think the apples need it (and they definitely will). Same with the cinnamon.
Serve the apples warm but not too hot.