My guess would be:
They traced the image on the cookie using a KopyKake and an edible marker.
it is a special maching that actually stamps the cookie; not an edible image. these machines are very pricey (thousands).... i forget what they're called
I would say definitely not edible paper. Way too nice. And my guess is that since they are all sooo perfect, it's not a KopyKake tracing, although possible. I would say it is either an edible ink stamp or airbrushing over a stencil.