The best way for a cheese monger to wrap cheese is with clear plastic. You can see exactly what the cheese looks like, and make sure there's no mold.
So what's the worst way to wrap cheese? Clear plastic wrap. It traps evaporating moisture that condenses into tiny pockets of water, providing the perfect environment for mold to thrive, and it's not the French kind of mold.
I've learned that if I come home from market and put plastic-wrapped cheese in the refrigerator, I might as well save a step and toss it straight into the garbage.
Instead, the first thing I do is rip off the plastic, check for any mold, and immediately wrap the cheese in wax paper, which repels the evaporating water from the cheese.
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SHOW ME HOW
To keep the wax paper from unfolding in the fridge and letting the cheese dry out, I wrap the package in aluminum foil, and write the abbreviated cheese name on the outside with a Sharpie, as in "Ched." Properly wrapped, a soft cheese can last up to three weeks in cold storage, and if it starts to get funky, I shred the outside layer, and replace the old wax paper with new.
Harder cheeses, like Parmigiano-Reggiano, can last two or three months if wrapped properly. If you shred Parmigiano, it will easily last two weeks in a glass container. Of course, American Parmesan, which we mockingly pronounce Par-MEE-zhun, will last considerably longer in that green shaker.