I would like to implement a server in Python that streams music in MP3 format over HTTP.  I would like it to broadcast the music such that a client can connect to the stream and start listening to whatever is currently playing, much like a radio station.
Previously, I've implemented my own HTTP server in Python using SocketServer.TCPServer (yes I know BaseHTTPServer exists, just wanted to write a mini HTTP stack myself), so how would a music streamer be different architecturally?  What libraries would I need to look at on the network side and on the MP3 side?
Since you already have good python experience (given you've already written an HTTP server) I can only provide a few pointers on how to extend the ground-work you've already done:

Prepare your server for dealing with Request Headers like: Accept-Encoding, Range, TE (Transfer Encoding), etc. An MP3-over-HTTP player (i.e. VLC) is nothing but an mp3 player that knows how to "speak" HTTP and "seek" to different positions in the file.
Use wireshark or tcpdump to sniff actual HTTP requests done by VLC when playing an mp3 over HTTP, so you know how what request headers you'll be receiving and implement them.

Good luck with your project!
Writing a Python Music Streamer