I searched for quite a while for how to store Parmesan. Mine was molding before I could use it up. I did scrape the mold off, but I wanted a better solution. I was wrapping it in plastic and that did encourage the mold. Couldn't breathe. Now I wrap in parchment first and then put it in a ziploc bag. Haven't had any problems since.
Never put off till tomorrow what you can screw up today.