Preheat oven to 425° F.
Spread bones in a roasting pan and roast for about 30 minutes, turning once. Remove from the oven, and paint a thin layer of tomato paste over the bones.
Put the vegetables on top of the bones, and roast an additional 15-20 minutes, until the vegetables begin to caramelize.
Remove the bones and vegetables to a stock pot.
Deglaze the roasting pan with wine or water, and pour this into the stock pot. Add peppercorns, bay leaves and thyme. Cover the bones with cold water.
Over medium heat, slowly bring the bones up to a very gentle simmer. Don’t let the stock boil.
Adjust the temperature to maintain a gentle bubbling.
Every thirty minutes or so, skim off any foam that rises to the top of the pot. Let the stock simmer gently for at least four hours.
If you have the time, it can simmer for up to 12 hours. Add a little more water and lower the heat if you are getting too much evaporation.
When the stock is done, remove the bones and discard.
Strain through a very fine mesh strainer or through a colander lined with three or four layers of cheesecloth.
Chill quickly, then refrigerate. Skim off the fat from that has solidified on top, and discard.