Rinse chicken bones and pieces. Pat them dry and set aside.
Heat oil in a large stockpot over medium heat. Add vegetables and cook, stirring frequently, for about 5 minutes, or until just softened. Stir in chicken carcasses and/or pieces, thyme, peppercorns, and bay leaf. When well combined, add 1 gallon of water. Bring to a boil, then lower heat and simmer for about 3 hours, occasionally skimming off scum, or until liquid is reduced to 8 cups.
Strain through a fine sieve, pushing on solids to extract as much liquid as possible. Discard solids. Allow stock to cool slightly, spooning off fat as it rises to the surface. Cover and refrigerate for up to 2 to 3 days, or freeze in small quantities, for ease of use, for up to 3 months. Before using, spoon or scrape off any fat that has solidified on top.
Recipe courtesy of Gourmet Magazine