I'm looking for podcasts that are similar in depth and sourcing to The History of Rome podcast by Mike Duncan or that are similar in nature to the audio recordings offered by The Great Courses, especially the latter, as the authors alone can be trusted based on their reputations (they're all taught by tenured professors of the subjects at hand). I included the Duncan piece because its received high marks from listeners and has an extensive bibliography.
Does the r/AskHistorians community have any good suggestions?
I am obligated, as the host and producer, to plug our very own AskHistorians Podcast, which features interviews with flaired users of this sub and the occasional outside academic.
While not exactly fitting the mold of the Great Courses, some podcasts featuring professional academics that I have enjoyed are:
15 Minute History from UT-Austin, featuring interviews with professors and grad students there.
Backstory, which is public radio program with three history professors covering a particular theme.
In Our Time from the BBC, which is a round-table discussion by a trio of academics on a particular topic, not always historical.
You might take a look at the people who presented at the history podcasting roundtable at AHA 2016, also a lot of people livetweeted that session under #s161, so lots of working podcasters talking to each other on twitter to take a look at.
iTunesU is pretty fantastic if you look around a bit. There's quite a lot of junk (I don't know who would give a damn about a 3 minute answer to a random personal question from some professor that some universities seem to think is worthwhile content), but if you look around there's gold as well. Oxbridge seem to do particularly well with guest lecture series in history.
The other one I would point to, it's not a podcast per se and I've actually asked a question here if there are any equivalents (no responses unfortunately), but I love the YouTube videos put out by the American National World War I Museum and Memorial: https://www.youtube.com/user/NationalWWIMuseum
A really great variety of academics with in-depth discussions on a whole manner of WWI topics.
Footnoting History is good - team of grad students