When asked how to smoke cheese my mind flies thru all of the complexities of cold smoking cheese.. something that is alien to most people. You have to cold smoke the cheese so it does not melt.
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By cold smoking we mean smoking at temperatures of 90 degrees or less something that can be quite difficult for the backyard smoker.
Armed with some knowledge and a little tenacity it can be done proficiently in the WSM smoker as well as in the larger wood fired smoker as long as you realize that heat must be kept to a minimum while the smoke must roll on.
Just about any type of cheese can be smoked including Swiss, Colby, Provolone, Mozzarella, Havarti, Jarlsburg, Stilton, Gouda and a host of others that I will refrain from mentioning at this time.
The trick is to let the cheese sit out in the open air for a bit before smoking to allow the outside to toughen.
You will want to light 3 or 4 pieces of charcoal and place it on top of oak, apple, pecan or other mild flavored wood chips to create ample smoke without too much heat.
You can also modify a wsm in such a way that makes the cool smoke low heat atmosphere a lot easier to achieve.
Here is a newsletter that I wrote on smoking cheese. This article is very informative on smoking cheese and shows you a couple of devices that easily create smoke without heat to enable the low temperature required.