what's the best way to store parmesan cheese?

wrap it in fine cheesecloth, a fine open weave cotton- buy them at a kitche store, and put the cheesecloth on a piece of stone, and put that in a cool place but NOT neat the fridge door- every time you open the door, the moisture will start to from drops of water. It should be kept cool and dry, NOT in a moist area, and unfortunately that's waht happens when you keep opening the fridge door- so make sure it's at the bac of the fridge or something.

I wrap my parmesan and romano cheese's in a piece of paper towel, and put them in a sealed container, glass it preferable as plastic will absorb the aroma, as chef I had the opportunity to use some really aged stuff, 5 & 10 yr old parmesan, and it is pungent, just grate it fresh eat time and store back in the frig as previously stated, it is like fresh pepper, only do as much as you need, and ever boil a sauce with it or it will curdle and the milk proteins will go stretchy.

Wrapped in the fridge, it will go hard on the edges at room temp.

Or tie it to the belly of your favorite goat, It should stay moist for months, and develop a delightful gamey aroma. This is the traditional sicilian way.

After I open the container, I place it in a refrigerator and the cheese stays good for a long time.

Probably at room temperature. You'll get the most out of the flavor that way because it won't be cold.