:^) They didn't cook animals whole, AFAIK -- they'd butcher it out into strips and use natural dessication (wind, cold) to produce jerky, then cut off or bite away.
I’m sure they used a variety of techniques. American Indians would immediately eat raw liver of a large animal. Most nutritious part of the animal and rather perishable. I’m sure some were chunks roasted over fire. For large groups probably a pit roast, and the drying and pemecin type sausage making for long term supplies.