Let's start with an observation, these crusts are generally hard as wood!
You've done everything you can, but it's impossible to grate more, especially by hand, too hard, and you risk hurting your fingertips with the grater by pressing too hard.
Should the crusts be thrown away? No, that would be a real shame, but then how to use them? Here are some tips.
In a hot and liquid preparation
It is very simple, as soon as you prepare something hot and liquid, a soup, a gratin or a sauce for example, add your croutes from the beginning of the cooking and let them perfume deliciously your preparation all the time of the cooking. Remove them before blending (soups) or using, note that they have become soft and can be eaten.
Some examples of recipes where you can use these croutes: Potato
gratin (in the milk with the potatoes),
béchamel sauce (also in the milk) or
leek-potato soup (when you add the water) and
gratin with parmesan flavours.
In the oven
You can put your croutes in the oven for a few minutes at 180°C (360°F), they swell and become crispy, to be served as an aperitif for example.
Olive oil with parmesan
Cut your croutes into small pieces, put them in a jar with a lid, cover with olive oil, and let them macerate for at least 15 days. The resulting parmesan oil will give a pleasant flavor to your sauces or pasta dishes.
To sum up: Do not throw away the Parmesan cheese crumbs, it would be a pity, it is better to use them in cooking, either hot (soups, sauces, in the oven, ...), or cold (maceration in olive oil).