Is there a universal departure recovery procedure?
The answer depends on the aircraft. In most cases it is No, but for some it is Yes.

The MiG-29 has a green button at the right side of the stick which recovers the aircraft to a wings-level, shallow climb attitude if pressed. Note that the MiG-29, unlike its Western counterparts, is aerodynamically stable over the full angle of attack range beyond 90° and the flight control system can recover the aircraft from any attitude, altitude and thrust permitting.

Here is a quote from someone reporting his experience of flying a Malaysian MiG-29 (link)


  The stick has a red autopilot button on the left and a green auto
  recovery switch on the right for the disoriented pilot, and works by
  pressing the green panic button. The system recovers the jet to wings
  level and places the airplane in a slight climb if energy is
  available. This system is known to be reliable but is not often used.
  This is most likely due to the necessity of having to recognize that
  you are spatially disoriented prior to pushing the auto recovery
  button.




MiG-29 cockpit (picture source). The green button is clearly visible.