As we've discussed above, when you say "we want to let them use [our library of controls]", the devil is in the word use. If you're asking "can we let the members of this project run our code without having to pay for it", then the answer is of course "yes".
But I suspect that what the project wants is to incorporate your library into their project, which they distribute freely. At this point, one of two things happens: either you give them the right to redistribute your code under the MIT licence they use, in which case, your library's going to turn up in competing commercial projects quicker than you can say "AGPL"; or you allow them to use your library but only distribute it in binary form, in which case their project becomes non-free, and I suspect, non-usable.
Is it possible to license commercial software to a MIT-licensed project?
Yes, but it's not possible to license it under a weakly-free licence like MIT and retain control of your software.
What is the best way to do this?
Best is a subjective word. If it were me, I'd agree they could use my library, but only under a strong copyleft licence, such as GPLv3, or even AGPLv3. That might well mean they had to distribute their project under the same licence, a consequence that they'd have to decide whether they could endure. But it would mean that no competitor could scoop your library out of the MIT project code and lock it straight back up again.
Are there any good examples of where this happens already?
Examples, yes, but again, good is a subjective word. Examples I consider good you might consider terrible, because of the licensing implications for the formerly-proprietary code.