Put the chicken back and breastbone, parsley, celery, carrots, garlic, onions, tomatoes, peppercorns and bay leaves in a large (6-quart) pot. Add water to cover completely, and bring to a boil over medium-high heat.
Reduce the heat to low and cook at a bare simmer, skimming the scum from the surface periodically and adding additional hot water as needed to keep the ingredients submerged, until the stock is flavorful, about 1 1/2 hours.
Strain the stock through a fine-mesh sieve, and then divide it between two containers to cool quickly. Let cool completely before freezing or refrigerating. The stock keeps for about 1 week in the refrigerator and for many months in the freezer.