Parmigiano keeps well, if you wrap it tightly each time, it can easily be stored in the fridge for at least a month, though I am not sure if it can be done for any longer period, our chunks are usually gone by then. Sometimes when we find them on sale, we buy in larger amount, cut them in small cubes so they will fit better inside our cheese grinder, put it in a plastic bag and freeze them. True, the texture suffers a wee bit if you decide to be picky, and to snack on as it is, it is definetely better unfrozen. However it is more than sufficient for dressing your pasta and risotto.