MFL Recording - Cover Reference?

As we're about to leave for a NY trip, including My Fair Lady, I need your help for pre-show brunch discussion....

I keep remembering a speech from a gay play about seeing the famous Hirshfeld cover of the MFL cast recording with the heavenly creator pulling the strings to Henry & Eliza puppets. Interestingly, at various times, I can picture characters by McNally (L,V,C!), Tony Kushner (AiA), or Paul Rudnick (Jeffrey) all giving that speech.

What was the play and character?

Thanks!

Updated On: 9/2/18 at 12:27 PM

It is indeed from Rudnick's "Jeffery" delivered in the film by Nathan Lane as Father Dan.

Thanks - and I pictured Nathan Lane delivering it. (Which I guess would've left AiA out - also because it would have to be Louis and would've been Jewish)