If you are regularly splurging on beautiful craggy pieces of Parmigiano-Reggiano (or, it’s more local cousin Parmesan), you should enjoy every last bit.
That includes the rind!
As a wheel of Parmigiano-Reggiano ages, it develops a natural protective layer that, over time, becomes dry and hard. That layer is full of condensed cheese-flavor that can be used as a bonus ingredient. Though it is technically edible, the rind is too tough to chew, but you can use it in cooked preparations.
Sauces
Many tomato sauces and ragús include Parmigianno-Reggiano rinds to add body and savoriness. Simmer a rind (or more, depending on how much you are making) while the sauce cooks and discard the rinds before serving.
Soup and Stews
You can add a rind or two to any soup or stew for a subtle salty and savory addition, like Minestrone. Add the rind when you add the broth and leave it to simmer until the soup is ready. Discard the rind before serving.
Broth
Use a few rinds (about 4) to make a flavorful broth to use in other dishes, like for risotto, vegetable stews, or as the base of a pan sauce. Simmer the rinds with water and some aromatics, like onion, carrots, and herbs for at least an hour. Strain it when it is flavorful.
You can use leftover rinds right away, or store them in a zip-top bag or container in the freezer. Specialty stores, especially ones with good cheese departments, often sell rinds. Be sure to ask!
Be sure to stir any pot that includes a cheese rind from time to time. Bits of cheese can melt from the rind as it cooks and may burn at the bottom of the pan if not stirred occasionally.