We made some apple smoked cheese a couple days ago on the Big Green Egg. We chose to make Sharp Cheddar, Monterey Jack, and Colby The challenge with smoking cheese is keeping the grill cool enough to not melt the cheese and make a mess. Of course you can get the apple chips from: Colorado BBQ Supply
One simple method is to use a small amount of charcoal and use the cold weather and cold grill to your advantage. I use a small cast iron smoker box to hold some charcoal placed in the bottom of the grill.
Next step is to light the charcoal with a Mapp or Propane torch. Once the charcoal is just lit enough to make smoke, throw a handfull of apple chips onto the lit charcoal.
Inset the indirect setup, I use the platesetter and also the pizza stone for cold thermal mass to soak up any direct heat from the smoldering of the apple chips and charcoal.
Place your cheese on the main grate and smoke for about an hour or so. Be sure to close down vents enough to prevent the wood chips from actually catching fire.
Once the cheese is pulled from the smoker, it is best to vacuum seal it and let it sit for a week or longer to mellow. When the cheese is first smoked the smoke flavor remains near and on the surface and is really strong and overpowering. After mellowing in the vacuum sealed bags the smoke flavor works into the block of cheese and becomes uniform and flavorful.
The finished product before going into the fridge for a week: