1. Preheat oven to 375 degrees.

2. Place chicken parts in a large stockpot. Pour enough cold water over chicken to cover by 2 inches. Place pot over medium heat and bring to a boil. Cook chicken for 5 minutes, skimming off any impurities and foam from the surface. Drain chicken, rinse, and transfer to a roasting pan.

3. Drizzle oil over chicken and toss to combine. Transfer to oven and roast chicken, turning occasionally, until golden brown, about 35 minutes. Add leeks, onions, carrots, and celery to roasting pan and toss to coat with oil. Return to oven and roast mixture until vegetables are caramelized, about 20 minutes. Add tomato paste and toss to coat chicken and vegetables.

4. Transfer contents of roasting pan to a large clean stockpot and cover with enough water to cover chicken mixture by 4 inches (about 6 1/2 quarts of water). Add 1 tablespoon salt. Bring to a boil over high heat. Reduce heat to a simmer and cook for 90 minutes, frequently skimming off any impurities from the surface. Add bay leaves, thyme, and peppercorns, and continue cooking and skimming surface for 30 minutes more. If cooking liquid starts to evaporate below the level of the solids, add enough water to cover.

5. Remove stockpot from heat and let stand until all solids sink to the bottom of pot, about 15 minutes. Ladle stock through a fine mesh sieve set over a large airtight container; discard solids. Let stock cool and use right away or cover and refrigerate for up to 3 days, or freeze for up to 3 months.