This is a little off the beaten track, but it may be useful in some cases.
Boil the rind in water, and then reduce.
This is the way to make (very expensive) liquid parmesan. You grate a load of parmesan, boil it in water, and then sieve out the cheese matter. What you are left with is a mixture of water and parmesan-flavored oil, from which you can remove most of the water by gently boiling it off.
This is probably where most of the benefit of adding the rind comes from. There isn't much solid cheese matter on it, but a lot of flavor and oil. This means that an alternative approach is to separately boil the rind in water (just enough to submerge it) and then to boil most of the water off, and add the remainder to the sauce.
It's a bit more involved than just dumping the rind in the sauce directly, but it has some benefits:
- You can boil the rind until long after it breaks up, extracting as much flavor as possible. All you need to do is sieve it out afterwards.
- You can store the resulting liquid to directly add to sauces. Save up your parmesan rinds for a while, make one batch of parmesan liquid, and then store this in the fridge so you can add a bit of it to every sauce you make.