The OM for Mechanics is the AMM.
There are two shut down procedures:
Stop the Engine Procedure (Usual Engine Stop)
If you cut off the fuel before wating the 3 minutes cooldown periode you can compare it with a flameout not caused by an engine failure:
Stop the Engine Procedure (Emergency Engine Stop)
So in my (technican) point of view, 3 minutes are minimum.
Shutting down without waiting the whole 3 minutes normally not end in a extreme damage of the engine, but lifetime and performance are reduced.