At the current time, one could go to this page: http://www.morethankitchen.com/product/1872696030 and legally view an image which appears to show the tool being used like a standard grater as you have described. Now that I see that your parmesan is very fresh/moist, perhaps the idea is to crumble it - sort of like making tiny versions of the chunks you would break off with one of these knives: https://commons.wikimedia.org/wiki/File:Parmesan_cheese_knife_on_block_of_cheese.jpg.