> However, it does not _immediately_ transmit classical information.
As I understand it, once you distribute an EPR pair, you can transmit one qubit of quantum information which thereby destroys the pair. Provided you can encode your classical information into quantum information, the amortized rate of classical information communication cannot be faster than light because you need to first distribute the EPR pairs (which you cannot do at FTL), but the _instantaneous_ rate of classical information communication could be faster than light.
The biggest assumption here is that you can encode/decode classical information to/from quantum information at a rate (if at all) faster than it would take for matter to travel over the potentially infinite distance between the EPR pair. Some googling reveals that this is possible via means such as time-bin encoding. (Edit: time-bin is only for photons, which I don't know if you can entangle, but it still appears that you might be able to encode classical information in electron spin)
What am I missing?
Edit - alecco's other answer in this thread make it much more clear what is going on. Thanks again.
It sounds like you already figured this out, but you can't encode classical information into the system in such a way that would allow for FTL transfer of information. Depending on what you are specifically thinking of as "encoding", there will be an equivalent reason why it won't work; often because you collapse the wave function of your local quantum pair-element when you transfer energy into it, which is a form of observation.
First paragraph.