Scatter the reserved bones in a baking dish and bake for 15 minutes.
Scatter the vegetables over the bones and bake for an additional 15 minutes.
Transfer the cooked bones and vegetables to a saucepan. Add some water to the roasting pan and deglaze over heat. When all the caramelized partials are loose, transfer them along with the water to the saucepan.
Add sufficient water to the saucepan to cover the bones plus another 50 percent. Bring the water to a boil. Reduce heat to simmer.
Simmer the contents for about 2 hours until the liquid is reduced by half. Skim any scum that forms on the surface.
When reduced, strain the stock through a strainer and then through a chinois. Check the volume of the stock. If it is greater than about 200 milliliters, reduce further.
Refrigerate strained stock until needed. Remove and discard any fat that congeals during cooling.