Real Parmesan cheese, Parmigiano Reggiano, is expensive stuff. It's a lot cheaper in and around Parma, costing 1/2 what it costs at CostCo, which is the best price I've found in my neighborhood. I would have brought home a whole wheel but that's a heavy hunk of cheese to drag around Italy. And if you are not in Italy, it's not exactly cost effective to jump on a jet.
So, you want to get your money's worth. What? You don't buy real Parmesan cheese? Yes, it is a luxury item but a little bit goes a long way. There's a reason Parmigiano Reggiano is called the King of Cheeses. Its nutty salty flavor is irreplaceable. Though Romano and Grana are worthy cheeses, they are not Parmigiano. American imitations of any of these Italian cheeses are poor imitations, made in vast quantities and sold for next to nothing (relative to the real thing). Don't do it! Buy the real McCoy and use every bit of it.
That means the rinds too. They freeze great; they will last forever in the deep chill. Even if they have dried out in the fridge, keep them. They are fantastic added to soups. Not only do they add great flavor, they are a wonderful textural addition. Every bit of the rind is edible with proper treatment. The rind is just dried-out hard cheese. After long cooking in a soupy environment, the hard cheese turns into this gooey, unctuous deliciousness. The best use of the rinds, then, is immersion is a brothy soup such as a minestrone, or a long-cooking tomato sauce. It does take a while for the cheese to rehydrate so you need to give the cheese enough time to soak up moisture and melt into a tasty goo.
Here's a simple minestrone from the excellent book, Fagioli by Judith Barrett, on beans done the Italian way. Those Parmesan rinds will go to good use here.
Minestrone of Chickpeas (Cicerchie)
2 cups Chickpeas
1 rib Celery, finely chopped
1 medium Carrot, finely chopped
½ cup Extra Virgin Olive Oil
1 medium Red Onion, finely chopped
3 Yukon Gold Potatoes, peeled and cut into a small dice
6 chunks Parmesan Cheese Rind
Salt And Black Pepper
6 Plum Tomatoes (About 1 Pound), cored, seeded, and chopped
15 stems Flat-Leaf Parsley, leaves only, finely chopped
Extra Virgin Olive Oil, for garnish
Soak chickpeas in cold water overnight. Drain and discard the soaking water. Rinse under cold water and drain again. Combine the beans with the celery, carrot, and 10 cups of cold water in a heavy 6 quart soup pot over medium-high heat. When the water begins to boil, lower the heat and simmer, stirring occasionally, 1 to 2 hours, until the beans are tender.
Heat the olive oil in a medium saucepan over medium heat. Add the onion and potatoes and cook, stirring, about 5 minutes; add to the beans. Add the Parmesan rinds. Continue cooking about 30 minutes longer. The beans and the rinds should be quite tender. Season with salt and pepper to taste. Stir in the tomatoes and parsley and cook 5 minutes longer. Serve with a drizzle of extra-virgin olive oil.
Link to PDF of Minestrone of Chickpeas recipe