Miui for the Desire would call record out of the box, because the kernel was built that way, I also loved the battery bar across the top. Because it is such a deep seated software requirement apps can't really record the call, they can record outgoing clearly, but have to rely on the speaker for picking up the incoming.

Which simply put is pants. I think the best thing you can do is lobby Muiu to support the One.

 

MIUI has apparently been ported to the One: http://forum.xda-developers.com/showthread.php?t=2352742. Don't know whether it supports the feature (it's already a long thread, and I've only read a few posts), but it's there to try.

Root alone doesn't give you features like this, which as IB says need support built into the kernel. What it does give you is the ability to install such a kernel once someone writes one. I guess the best is to keep an eye out for a custom ROM saying that it supports it.

I guess Sammy must have added that, as it's not a stock android feature to my knowledge.

 

Android Revolution 12.1 now has the option to record calls (it's an option in Aroma).

It's not perfect but it does work and saves the file in the Voice Recorder app.

Android Revolution ROM's are always as close to Stock as you can get them with extras just as add-ons.

I think this might suit you perfectly.

• 
  [*]Based on latest HTC One 2.24.401.1 (WWE) firmware that includes:
  - Android 4.2.2
  - Improved BlinkFeed
  - Stock HTC %battery
  - Stock HTC EQS
  - Lock-screen widgets
  - Long press home button works as menu
  - Possibility to remove all icons from the dock
  - Icons doesn't disappear from the app drawer even if added to the dock
  - Audio improvements
  - Camera improvement
  - Thermal configuration improvements
  - Much more!
  [*]Added Advanced Power Menu in AROMA installer
  [*]Added Call Recorder feature in AROMA installer
  [*]Added Exchange Security Disabler in AROMA installer
  [*]Added Volume Wake-up mod in AROMA installer
  [*]As always credits to shnizlon for above AROMA mods
  [*]Updated Dropobx, Facebook, ES File Explorer, Twitter
  [*]Updated Chrome, Maps, Music, Google Plus
  [*]Removed Mocana KeyVPN app
  [*]Other minor changes and fixes
  [*]Included and updated components:

 

Pretty solid release ... it works best if you update your firmware and radio to match. Guide and link to the correct files here >> http://forum.xda-developers.com/showthread.php?t=2365506.

Don't Skip the section on flashing the "New" recovery after the firmware update. (touch driver changed)