Preheat oven to 350°. Lightly coat the bones with 1/4 cup of the oil. Put them in a roasting pan and roast, turning occasionally, for about 20 minutes, or until well browned. Using a slotted spoon, transfer the bones to a large stockpot.
If necessary, add the remaining 2 tablespoons of oil to the roasting pan. Stir in the vegetables and cook over moderate heat on top of the stove, stirring frequently, for about 5 minutes, or until the vegetables are softened. Using a slotted spoon, transfer the vegetables to the stockpot.
Pour the fat from the roasting pan. Add 2 cups of water and cook over moderate heat, stirring constantly and scraping up any particles sticking to the bottom of the pan, until the pan is deglazed, about 2 minutes. Pour the mixture into the stockpot. Add the remaining ingredients and 3 1/2 quarts of water and stir to combine. Bring to a boil, then lower the heat and simmer for about 6 hours, occasionally skimming off any foam and fat, until the liquid has reduced to 6 cups. Strain through a very fine sieve, pushing on solids to extract as much liquid as possible; discard the solids. Let the stock cool slightly, spooning off fat as it rises. Cover and refrigerate for up to 3 days or freeze, in small quantities, for ease of use, for up to 3 months. Spoon or scrape off any fat that has solidified on top before using.