In a deep pot over medium heat, heat oil. Add onions and garlic and cook until limp and aromatic. Add chicken and cook, stirring occasionally, for about 5 to 7 minutes or until chicken changes color. Lower heat, cover, and cook for about 15 to 20 minutes or until chicken releases its juices.
Raise heat to high and add boiling water. Add bay leaves and peppercorns. Season with salt. Skim scum that accumulates on top. Lower heat and return to simmer for another 10 to 15 minutes or until chicken is cooked through.
With a slotted spoon, remove chicken pieces from broth. Allow to cool to touch. Remove meat from bones and shred. Set aside chicken meat and keep warm. Break bones to expose marrow and return to pot.
Continue to cook at barely a simmer, uncovered, for about 1-1/2 to 2 hours or until liquid is reduced and concentrated. Using a cheesecloth, strain stock to remove bones and aromatics.