Grill the carcass on all sides to get some char on the chicken.
Combine all ingredients in a large stock pot.
Bring to a simmer on the stove top and reduce the heat. Cook over medium-low heat until the liquid is reduced by half.
Line a mesh strainer, or colander, with cheesecloth. Pour the stock through the strainer. Discard the solids.
Cool the stock to room temperature in a large container, with as much surface area as possible. Chill in the fridge, then transfer to a storage container.