I eat the cheese as a snack. I put the rind in the minestrone. I use a lot of parmigiano so I don’t have to buy the rinds seperately–I just cut them off and freeze them in a plastic "freezer bag" for when I’m making soup.
By the way, the cheapest place I’ve found to buy Parmigiano Reggiano is CostCo ($7.99 a pound as opposed to twice that at the supermarket and more at "gourmet stores"). And they sell a very good grana padano for even less (and the rind should be very good too).
Trader Joe’s is cheaper than supermarkets too. Mine usually has Reggiano for around $11.99/lb.
By the way, for anyone not familiar with grana padano: