The cooking method meaning came first, though interestingly originally spitchcock (as it was originally spelled) referred to splitting an eel along the spine for cooking. Its origin before that is obscure, but alteration of split + cook seems likely. Although I marked only one of the metaphoric extensions as British, only the cooking term is generally used in America.
He plucked, cleaned, and spatchcocked the grouse before I finished laying the coals, and was grousing about the slowness of hardwood.
---L.