Your father would make a gift of the offender's heart to the injured party. As the injured party here is the city itself, the heart would be removed and allowed to burn in the sunlight and the ashes spread through the city.

[ That- makes the whole thing sound rather more clean and elegant than it is. 'Removed', as if it were just a fine, something being taken from them. As if it were not 'the ribcage wrenched open and the veins and arteries cut through with claws to remove it'. ]

I- don't think it would be safe to consider a cleaner method. Not at present.