AlexxKay wrote: The most common (only?) monster with "fast regen" also has Cowardly, so it's tricky to work out what's happening with him.
They have cowardly and
knockback, making them actually one of the most complicated monsters in the game. There are other monsters with fast regen, though. The Toll Troll of Havensdale Bridge and Changelings (only when playing as a Monk; their special ability changes based on your class) come to mind.
And while the tooltip for Burndarayz says that it slows regeneration, it doesn't say by how much. (Some quick experimentation showed that it definitely didn't stop it altogether.)
It's -1 HP per tile. This means it's relatively more effective against low-level monsters.