The following is from the Kohler Courage engine Owner's Manual that you can download from the Internet. So whether you let it idle, as I grew up doing with all gasoline engines, or whether you shut it off at high speed depends on whether or not yours has the shutdown solenoid.
Stopping
1. Remove the load by disengaging all PTO
attachments.
2. a. For engines without a shutdown solenoid:
Move the throttle to the slow or low idle
position. Allow the engine to run at idle for
30-60 seconds; then stop the engine.
b. For engines equipped with a shutdown
solenoid: Position the throttle control
between half and full throttle; then stop the
engine.
Incidentally, maybe one time in ten, when I shut mine down, after the engine quits turning, I get one loud backfire pop. The dealer says that solenoid is sometimes sticking, but he doesn't think it will hurt the machine.