There's a dispute about whether to use plastic wrap, wax paper, aluminum foil, zip-loc bags and so on. Also, I've heard that its a good idea to take the cheese out and let it breath from time to time.
Any washed rind cheese care advice?
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Your best bet is probably a specialty product intended to wrap chese—that is, cheese paper.
Cook's Illustrated tested and found that (for cheese in general), wrapping the cheese first in wax or parchment paper, then over-wrapped loosely with aluminum foil performs better than either alone, and almost as well as cheese paper.
They report that the wax paper-aluminum foil wrap kept brie and cheddar almost as good as new for over a month.
They also found that plastic (either bags or wrap) developed mold before any of the other methods.
(Unfortunately, unless you have a Cook's Illustrated online subscription, you won't be able to see that link.)
I make artisan cheeses and here is my answer:
If it is a hard cheese (parmesan or cheddar like) just keep it dry, cool and not exposed to the elements..a plastic container of ANY kind is fine.
If it is a fresh cheese or soft cheese it needs some space to breathe and not get "wetter" than it already is. Keep it in a plastic container with a paper towel in the bottom.
Really...storing cheese (unless you mean for months) is pretty much just simple common sense.
If you are storing it for months than do some research on aging conditions (affinage) for the particular type of cheese you want to store.
Cheese papers are for bries and camemberts primarily. The average consumer had no need for them. Period
Sadly, nothing anyone can say will end that dispute.
Some things to keep in mind when storing most cheeses (other than, perhaps, fresh cheeses like ricotta):
(1) Cheese is alive with the yeasts, lactobacilli, and/or other wee beasties that helped to make the cheese, and they are a big part of your cheese's defenses against bacterial invaders. They need oxygen to survive. If the cheese goes anaerobic, the cheese will get funky in a not-so-pleasant way (likely sulfur, perhaps ammonia). It is therefore a good idea to store the cheese in a way that it can get a little oxygen. Just taking it out once in a while probably won't be enough.
(2) Wee beasies other than those that made the cheese (the molds, mildews, and other bacteria in your fridge) would love to munch on the cheese, given the chance. They are helped if the cheese is kept in a moist environment, or in a place where condensation will collect next to the cheese. Plastic bags and wrap are probably the worst for this, but that doesn't mean you should never wrap cheese in plastic, just be careful not to let water collect.
(3) Fats are like velcro for odors. If you keep your cheese on just any old shelf, then the cheese will quickly begin to resemble last night's salmon mixed with Tuesday night's Chinese take-out. Better to use a cheese drawer or, if your refrigerator does not have one, then get a plastic box and punch a couple holes in its lid.
(4) Finally, cheeses with a rind will deteriorate faster once the rind is cut, so get only as much as you expect will be eaten in a couple weeks.