Organisations warn many more people could be executed in the wake of the anti-government protests which swept Iran earlier this year.
The stories of Blackbeard and a man who was mauled to death by a lion are told in the new podcast.
The new law, passed on Monday, was pushed hard by the far-right and Security Minister Itamar Ben-Gvir.
Charles Burton was involved in a store robbery in which his accomplice shot and killed a customer.
Reports in January had said he was due to be executed after his arrest in connection with anti-government protests.
In a highly controversial move, some Israeli MPs are trying to introduce the death penalty for Palestinian attackers.
The judiciary says Soltani is not facing charges carrying the death penalty, while a rights group reports that the execution has been "postponed".
The US president does not rule out military action in Iran, as Tehran temporarily shuts its airspace to nearly all flights.
Iranian officials say Soltani, 26, has not been sentenced to death.
