Barbara's post reminded me that vinegar is a good way to keep cheese. There is an old fashioned cheese keeper--they used to be on the counters of the "general store". It is a large glass vessel with a ridged bottom. Vinegar was put in the bottom and the cheese then put in to rest on top of the ridges.
Hence, if you moisten a paper towel with vinegar and wrap your cheese, it will help preserve it also.
Personally I would not freeze parmesan. Freezing hard cheeses (chunks) changes the texture and makes them very crumbly. While parm is hard and dry, it still has a moist component to it when you shave it. I think this woud be lost if it was frozen. I have seen this happen with cheddar.
Hence, if you moisten a paper towel with vinegar and wrap your cheese, it will help preserve it also.
Personally I would not freeze parmesan. Freezing hard cheeses (chunks) changes the texture and makes them very crumbly. While parm is hard and dry, it still has a moist component to it when you shave it. I think this woud be lost if it was frozen. I have seen this happen with cheddar.