I actually had the chance to see fortune cookies made at the factory.
The machine had a series of heated dies much like waffle irons which rotated around the machine. Batter was metered in, the top of the iron shut and it moved around the base while it baked. After one revolution it was done and the top opened automatically. The operator flipped the flat cookie out, dropped a fortune slip on it, folded it over a peg placed for that purpose and dropped it in a bin. The motion was like starting to fold a taco, then bending it backwards around the peg and sliding it off.
This process yielded a finished cookie every 2 -3 seconds.