So I googled a little and found a fascinating neuroscience research paper - Speaker-listener neural coupling underlies successful communication. See Good connection really does lead to mind meld for a less technical overview and note the excerpt below (my emphasis in bold).
They found that speaking and listening used common rather than separate neural subsystems inside each brain.
Even more striking was an overlap between the brains of speaker and listener.
When post-scan interviews found that stories had resonated, scans showed a complex interplay of neural call and response, as if language were a wire between test subjects' brains.
It seems good conversation really does connect minds.