The BBC's In Our Time is excellent and they have a 20+ year back catalogue. The basic format is that the host Melvin Bragg (incredibly well-read in his own right) interviews three university professors about an event/topic/movement.

A couple episodes that I recall liking:

https://www.bbc.co.uk/sounds/play/b00fhp85 -- The Baroque

https://www.bbc.co.uk/programmes/b050bcf1 -- Thucydides

Surprisingly, nobody has yet shilled for the AskHistorians Podcast!

I would be remiss if I didn't plug my own history podcast (whose research has also informed most of my answers here), The Siècle, about French history in between the more famous epochs of Napoleon and the First World War.

I have listened to quite a bit of Hardcore History and would agree with the Quora answer you’ve linked in saying that Carlin is an excellent presenter of the stories he tells, but that his historical research and interpretation can be a bit lacking. What I’ve seen is that in his pursuit of the story of “extremes”, he often glosses over important facts (or leaves them out altogether) in favor of things that make for a more extreme retelling of the narrative in question. At the end of the day, I think that approaching HH as entertainment rather than a solid source of historical knowledge is a better course unless you’re interested in doing background research on the topics to separate facts from interpretation and speculation.

As for something I’d recommend, I have thoroughly enjoyed the History of English podcast done by Kevin Stroud. While I think it is technically a linguistics pod since it chronicles how we got from the very earliest stages of what would become English to the modern language, the historical research is deep and nuanced. In addition to the linguistic aspects (sound changes and the like), he also delves into the political, social, and cultural history surrounding the language. This dual approach makes for a unique narrative that has held my attention for years at this point, even through parts of history that have never particularly interested me in other tellings.

It gets off to a bit of a slow start, but if you stick around through those early episodes, it really pays off. There are currently 132 episodes that average about an hour each and the story is only up to the 1300s, so there’s still a lot to come!

I’m a world historian, so my picks are geared toward my interests and field, but some that I listen to regularly are:

Africa Past and Present . It’s interviews with academics sharing their research. I don’t subscribe but I check in from time to time to hear topics or academics I’m interested in.

Breaking History . I like this one because it’s put on by grad students and offers reading suggestions too.

Interventions. This is an intellectual history podcast put on by grad students as well but with interviews from the top academics passing through Cambridge University.

On top of the world . This is a podcast about world history but also about how to teach world history. A bit niche but covers really interesting topics (IMHO).

Tomorrow Never Knows. Great podcast that approaches topics through a gendered lens.

And most importantly, The Memory Palace . This is podcasting at its finest, Nate Demayo has the perfect radio voice and he does a deep dive into all sorts of history- putting you right there with living details. Best of all the episodes are all short, come out infrequently, and you are encouraged to jump all around and listen to episodes out of order.