I am playing Round Midnight by Thelonius Monk and I ran into a problem. If there is a C♭ and I am in the key of E♭ Major, which has a B♭, do I play a B♭ or just a B (since C♭ is technically a B)?
You play exactly what's written (provided it's written correctly!). If Monk had wanted a Bb played, wouldn't he have written a Bb dot in the Bb line or space?
He wanted a B played, but probably for technical reasons, it shouldn't be written in the B place, so had to be called Cb and written as such. One example of that might be if the chord Abm comes along. Ab major is spelled Ab C Eb. To make that minor, the 3rd needs flattening, making it Cb. Not B, which with the key sig. would automatically be played as Bb. Also not B natural, as that note does not feature in an Abm chord.