Gingerbread Men can be obtained from hostile mob-dropped Presents (and not player-created Presents) or Continuum Orbs, and otherwise, are not legitimately obtainable besides those methods. Lucky Bells can make obtaining mob-dropped presents easier.
When eaten, it recovers two hunger points (one hunger drum).
Gingerbread Man's data values are:
4183 (dec), 1053 (hex), 1000001010111 (bin)
Issues relating to Gingerbread Man are maintained on the bug tracker. Report issues for Gingerbread Man there.