I'll be honest, I'm not listening through "Kings of Kings" for a sixth time just to fact check Carlin specifically. That said, I can think of a few examples in Achaemenid Persian history that might fit the bill here. They all come from the reign of Darius the Great, partly because Carlin almost entirely skips the period of Achaemenid history that actually features rebellious Satraps on a regular basis. Open satrapal rebellions were actually strikingly un common in the first century of Persian rule, never happening at all until the 440s (Megabyzus in Syria) outside of princes competing for the throne or "rebellions" where someone backed the wrong contender in those competitions.

Part of the reason you can't quite remember might just be that the Achaemenids had some favorite methods of execution, which went in and out of style over time. So many of their punishments sound the same.

The chronologically first possibility is from the Civil War following Darius' coup for the throne. Roughly 3/4 of the Empire either opposed Darius or tried to succeed in 522-21 BCE, but a supposed descendant of the old Median kings named Phraortes was the greatest threat. In his Behistun Inscription, Darius lists 9 regions of resistance, and 4 were following Phraortes as their new leader. Upon Phraortes' defeat, King Darius says:

Phraortes was taken and brought unto me. I cut off his nose, his ears, and his tongue, and I put out one eye, and he was kept in fetters at my palace entrance, and all the people beheld him. Then did I crucify him in Ecbatana; and the men who were his foremost followers, those at Ecbatana within the fortress, I flayed and hung out their hides, stuffed with straw. (2.32)

Similar punishments are described for other major rebels at Behistun, notably Arakha, the Armenian pretender in Babylon. Arakha was defeated by Intaphrenes, one of Darius' co-conspirators in his coup. According to Herodotus, Intaphrenes himself was executed on suspicions of plotting a coup himself shortly after securing the Empire for Darius.

Herodotus reports that Intaphrenes and the other conspirators were permitted to approach the Great King at any time, except when he was having sex. Intaphrenes attempted to exercise this privilege, but refused to believe the servants who told him that Darius was otherwise engaged and burst into the King's bedroom mid-deed, supposedly the exact scenario they'd used to murder Darius' predecessor. Darius was outraged, suspecting Intaphrenes of making a bid go power and fearing a wider conspiracy. He summoned the other 5 conspirators, who assured him that they had nothing to do with this. Darius sentenced Intaphrenes and his whole family, excluding his wife, to death. Intaphrenes' wife convinced Darius to spare one son as well, but the rest were executed (Hdt 3.118-119). To the best of our extremely limited knowledge, Intaphrenes was not a Satrap though.

The confusion with Egypt may come from an event around the same time. The Intaphrenes affair played out in the early 510s, and some time after 515, Darius deposed and executed Aryandes, Satrap of Egypt, on suspicions of rebellion as well. Herodotus exact story is dubious for a number of reasons, namely that Satraps were supposed to build monuments in their territory. Some historians are also skeptical about the claim that Aryandes minted coinage because none have been found by archaeology, but I personally find that less convincing. Minting coins was a common feature of later rebellions and Aryandes mint did not last long enough to leave huge quantities of evidence. Herodotus wrote:

This Aryandes had been appointed viceroy of Egypt by Cambyses; at a later day, he was put to death for making himself equal to Darius. For, learning and seeing that Darius desired to leave a memorial of himself such as no king ever had, Aryandes imitated him, until he got his reward; for Darius had coined money out of gold refined to an extreme purity, and Aryandes, then ruling Egypt, made a similar silver coinage; and now there is no silver money so pure as is the Aryandic. But when Darius heard that Aryandes was doing so, he put him to death, not on this charge but as a rebel (4.166)

There are also two similar descriptions of other events in Persian history, though I know the second is not mentioned by Dan Carlin.

First, in Herodotus (3.153-160) provides a garbled account the two Babylonian revolts in 522 BCE is compresses them into a single event to tell the story of Zopyrus. Zopyrus mutilated himself by cutting off his nose and ears (as Darius did to Phraortes according to Behistun), and presented himself to the Babylonians as a Persian traitor to infiltrate the city. As a high ranking enemy officer, Zopyrus was given control of coordinating the Babylonian strategy, and he used this to throw the gates open for Darius' forces. The story itself is doubtful. Zopyrus bears a resemblance to the story of Odysseus mutilating himself to infiltrate Troy.

The second comes from Plutarch's Life of Artaxerxes (29-30) near the end of Artaxerxes II's reign. Crown Prince Darius got over anxious for his father's death, feeling that Artaxerxes had repeatedly made him look weak and preemptively sabatoged Darius' future reign. He and the disaffected noble Teribazus attempted to assassinate Artaxerxes in his sleep, but the Great King caught wind of the plot and set a trap. Typically, the king presided over trials for regicide, but Artaxerxes could not bear to watch and only returned to public life to observe the execution of Darius and his sons (the King's grandsons).