Go take a look at this post over at Gordon Bressack's My Mind and Welcome To It blog, which relates the joke as told by a certain character whose name will not be unfamiliar to the Theme Time Radio Hour regular...
I first heard this joke sitting around a table in an Italian restaurant in Studio City with several people all in the comedy business including Maurice La Marche (impressionist, voice of The Brain among many others), Billy West (voice of Stimpy and numerous others), John DiMaggio (most well known as the voice of Bender on Futurama) and Eddie Gorodetsky (well-known and prodigious comedy/sit com writer). Eddie told the joke and we all fell off our chairs laughing.Be sure to read the comments, which are as interesting - if you're interested in thinking about how comedy works, that is - as Bresseck's post itself.
Bresseck made the post just about a month ago, making you wonder when Eddie G. told him the joke. Recently? Was it on his mind because of the "Goodbye" show?
As another of the commenters notes, like all jokes, Big Orange Head has a multitude of variations, "no two joke-tellers tell a joke exactly the same way." Here's a video of the Big Orange Head joke, updated for the digital age.
Thanks to "zinzoe" over at the Expecting Rain forums for the lead.