Pour olive oil into the bottom of a large roasting pan; top with chicken carcass pieces, carrots, onions, and celery.
Roast in the preheated oven, stirring occasionally, until bones and vegetables are browned, about 1 hour.
Transfer roasted chicken bones and vegetables to an 8-quart stockpot. Pour wine into the roasting pan, scraping the bottom to release any browned bits of food; pour into stockpot. Add peppercorns, cloves, bay leaves, and thyme to stockpot. Cover the mixture with water and bring to a slow simmer. Set heat to low and simmer, straining off fat as needed, for at least 5 hours. Strain stock through a cheesecloth; refrigerate or freeze stock.