Heat the oil in a large stockpot over high heat. Add the onion, carrot, celery, and garlic, and sauté, stirring occasionally, for about 2 to 3 minutes.
Add the remaining ingredients and bring to a boil, skimming off the cloudy scum that rises to the surface. (Be careful not to skim off the herbs and peppercorns when you do this.) Reduce the heat to low and simmer, uncovered, for about 2 hours.
Skim the surface of the stock, strain through a large fine-mesh sieve, and allow to cool thoroughly*. Discard the bones and vegetables. Refrigerate overnight. The next day, use a spoon to remove any congealed fat from the surface. Freeze the stock in 2- or 4-cup containers or ice-cube trays for use in individual dishes. Keeps for 1 month.
Note: A good method of cooling stock quickly to avoid bacterial invasion is to place the hot stockpot in a sink filled with ice-cold water. When the temperatures have equalized, refrigerate the stock.
Yield: 3 quarts