Storing the Cheese
Parmesan has a very low moisture content which makes it imperative to store your chunk correctly. It will be happiest in a cool, damp cellar (10C -14C and 80% humidity) but these are hard to find nowadays, so keep your piece tightly wrapped in wax paper with a layer of either foil or cling film around the outside of the paper.
This way the cheese can still breathe but is kept airtight and should keep in the fridge as a premium eating cheese for up to two weeks then as a grating cheese for a further six.
Finally, whenever you take the cheese out of the fridge to use, try to leave it unwrapped for 15 minutes or so. Any moisture that has been drawn out of the cheese while in the fridge will be reabsorbed, keeping the cheese soft and preventing any mould forming on the cut surface of the cheese.