Quote Originally Posted by sandmote View Post
Steady Recovery
An injured cynocephalus often surprises those of other races with their ability to recover from wounds. You regain one additional hit die at the end of a long rest, and the maximum number of hit dice you can have is increased by one.
What size is the extra hit die? Remember, I can totally have a crazy multiclass character with one level in each class, so it can't be determined by class. Medium sized NPCs usually use d8s for their hit dice, so that might be an option.

Alternatively, whenever they spend hit dice to heal, perhaps they regain additional HP equal to their proficiency bonus.