[crazygringo]

As far as I know, we don't know the exact mechanism by which binaural beats are produced, but it does seem to be from FFT information.

The hair cells in our cochlea function essentially as a great big FFT -- this is well-established -- and so our source neural input begins with that. The brain doesn't have access to the underlying waveform at all, as far as I'm aware. It is incredibly sensitive to the timing from each ear though (just as FFT includes phase information).

You can read all about what we do know here:

https://en.wikipedia.org/wiki/Neuronal_encoding_of_sound

Our brain does perform advanced signal processing to condense sets of overtones into a single fundamental frequency, which even works in the case of a "missing fundamental", and binaural beats are conceivably explained by this mechanism. Though it could be a different mechanism at work as well, related to how we process audio spatially.