What you U.S. citizens miss is that the real Parmigiano Reggiano is made in a very small area of North Italy, with a very specific combination of grass, terrain, weather and manufacturing that make that unique feature you can't find anywhere else in the world. Just for example: if you move just a few kilometers outside that area, taste changes so much that, despite you are still in Italy, what you produce can't be called "Parmigiano" but, instead, will be "Grana Padano", will cost about half the price, and will substantially change the flavour of your food.
So, please don't call that yellowish substance "italian cheese", that's not. It's american product or, if you prefer, fake food. Wood-based or not.