I‘m wasting my time in one of the most beautiful places in Europe

Cool and dry place for sure. As you said the Parmigiano is an aged cheese and this makes simpler to store it, but if course you can't overcome a certain period, mainly if you opened the wheel.

Gaetano.
I think that one was 12 years aged. I try to seal it after drawing as much air out as possible, and put it in the controlled drawer at the bottom. Granted that piece had to be going on several months since I first opened it. It has to be near or past five months by now.