Off I went to figure out what STUN was.
It turns out that STUN stands for Session Traversal Utilities for NAT. Interestingly, STUN messages are sent in the lower overhead User Datagram Protocol (UDP) packets, not Transmission Control Protocol (TCP).
Still, what on the iPhone was using STUN?
Here's Apple's chart of port usage that calls out STUN.
Check off that we've learned something today.