In a large stockpot, heat the oil over low heat and cook the onion, carrots, and celery for about 5 minutes, stirring occasionally, or until softened but not colored. Stir in the herb sprigs, peppercorns, and bay leaves.
Add the bones and water to the pot. Bring to a boil over medium heat and skim any foam that rises to the surface. Reduce the heat to low and simmer gently, uncovered, for 2 to 3 hours, or until flavorful.
Strain the stock through a fine-mesh sieve into a large bowl. Discard the bones and vegetables. Set the bowl in a larger bowl or a sink filled with ice water to cool. When cool, cover and refrigerate until chilled. Remove the layer of congealed fat from the surface. Transfer to covered containers and refrigerate for up to 3 days or freeze for up to 3 months.
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