I would like to store data using google protocol buffers (another serialized format would work, too), and then have an UI to browse that data. Is there a C++ framework/API that
If you want you can use web ui to compose a protobuf message
https://github.com/Groterik/protobuf-webui
It is python project and it has a sample that executes http server composing desired message type of imported protobuf module. But it is python, so you can write simple workaround that imports compiled protobuf module dynamically and chooses message type in runtime.
You can overload postprocessing method so it would do some useful work with message (store to file, send by network, etc)