On a rimmed baking sheet, add chicken in one layer, and toss with 2 tablespoons oil.
On a separate rimmed baking sheet, combine onions, celery, carrots, and garlic. Add tomato paste and remaining 2 tablespoons oil, and stir to combine.
Roast chicken and vegetables until golden brown, about 1½ hours.
Add chicken and vegetables to a 15-quart stockpot, reserving pans. Pour drippings from chicken pan into stockpot. To vegetable pan, add about ½ cup wine, and scrape browned bits with a wooden spatula; add wine and browned bits to chicken and vegetable mixture. Add bay leaves, peppercorns, and remaining wine to the pot. Cover mixture with cold water.
Heat pot over high heat, and bring to good simmer. Skim foam occasionally with a ladle. Lower the heat to low, and allow stock to simmer for at least 4 hours and up to 6 hours. In the last hour, add thyme or other herbs you might have around.
After the cooking period, strain stock into a clean pot with a colander or China cap. Allow to cool for immediate use or freeze in plastic freezer bags for up to 4 months.
Notes
*Chicken wings can be substituted.
Recipe by Louisiana Cookin' at https://louisianacookin.com/brown-chicken-stock/