The browse control has two components, the actual browse button:
...and the browse dialog:
You can get to examples of both via Differential → Edit Revision.
These are both kind of ugly.
The browse button should probably be integrated into the tokenizer, like the mock in T5750, and just be an icon instead of an icon + text. I wasn't immediately able to get this working cleanly with bare PHUIButtonView.
The dialog probably just needs some tuning and cleanup.
(The dialog title also needs to use an actual human-facing string.)