Take the special ability with cooldown of choice, like savage strike.  Use it then keep moving the unit away so it won't get killed.  One turn before the ability appears to be usable again, you can use it if you click on another unit and then re-select the unit with the ability.

One more example of how info on the screen is not updated properly until something else happens, but its a little more than that, because you really can't select the ability and use it until you select some other unit and then come back.

This may be easier to test if you only have the one unit, so your turn will start with it selected.

This has been going on forever.