Looks like Persian has a language learning podcast too

It's called Chai and Conversation. It seems to be pretty much the same excellent format that these language learning podcasts use - two people get together to record a podcast together, listening to it is free, and bonus materials cost a tiny bit of money.

The podcast is recorded biweekly, and the latest lesson is Lesson 22. They are still going over some pretty basic concepts by then (how to count objects using تا, how to conjugate داشتن in the present tense) and the podcast focuses on colloquial Persian instead of literary.

This means that for the time being if you're really focused on getting to fluency in the language you're going to want to use a site like this to help make it happen.

One other good thing about the site: the note on why they use the term Persian instead of Farsi, with which I agree 100%.