AskHistorians has its own great podcast that covers a wide range of topics.

and a lot of the history podcasts I found feel pretty ... Superficial

can you list them so we can get an idea of what you're not looking for?

edit: the british history podcast is a good choice

Revolutions.. He's covered the English and American Revolution. Currently on the French Revolution and that's going to take about a year total.

http://12byzantinerulers.com/ http://normancenturies.com/

I know it's not as broad as you would like, but I hope this will quench your thirst somewhat.

Just like to add "The infinite monkey cage" (can be found on youtube and iTunes, but you gotta pay there). It covers a wide range of topics including history.

The BBC's In Our Time programme is in my opinion the best 'podcast' out there. The discussion is in depth, analytical usually features experts in the field. It's been running usually weekly since the 90s so there are hundreds of episodes on a wide variety of topics.

The archive can be found here: http://www.bbc.co.uk/programmes/articles/2Dw1c7rxs6DmyK0pMRwpMq1/in-our-time-archive