Our fore fathers tried that.
The receipe requires you to stuff it with 3 x 1" stones .
Cook till stones are tender discard bird eat stones & save broth for latter.
We have actually created a monster by providing them with more habitat than they had before we got here so the numbers are something like 100 x what they should be.
Same goes for nearly all of the parrots except the ground breeding ones ( buggies for instance ) which dogs, cats & foxes have all but wiped out.