What I'm trying to get at is the *external* UUI - the one the carrier sends in as the identifier towards CUBE. I'm aware of the CallData.UUI but have a concern that the value in that field may be an "internal" UUI and not the outside UUI.
This link has some details on the external vs internal:
The session identifier is supported in CVP 11.6 and CVP will pass it to all the outgoing SIP messages, however to satisfy your requirement the Voice Browser need to handle the session id and pass it to VXML Server so that you could get it accessible through your Studio application.
I am not sure about the VXML Gateway behaviour for this, its not implemented in VVB yet.