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:
"Well, what's the difference?"you ask. Primarily the forage; the meadows in the production area between Parma and Reggio have certain grasses, while those of the meadows of the section of Lombardy that produces Grana have others. As a result there are slight differences in flavor and color (Grana is paler). However, though advertisers may say one is "better"than the other, the difference between pieces of Parmigiano Reggiano and Grana Padana that have been made with equal care will be stylistic rather than qualitative. You may prefer one, and your friend the other. It is true that Grana has more of a reputation for being industrially produced, and that it may be easier to find hand-crafted Parmigiano, but it's also true that industry is making inroads in Parmigiano there are cheese makers who hand-craft Grana Padano. So for every-day use you should find either quite satisfactory; Fernanda Gosetti suggests one use Grana in recipes that call for the cheese as an ingredient (as opposed to having it grated at the table) because it is generally somewhat cheaper.