To prepare the terrine, season the chickens with salt and pepper, then cold-smoke them for 1 hour. 

Preheat the oven to 350°F.

Place the chickens in a roasting pan, transfer to the oven and roast until an instant-read thermometer registers 150°F. When the chickens are cool to the touch, remove the meat, discarding the skin and bones, and shred the meat. Place in a bowl and set aside. 

Place the roasting pan on the stovetop over medium heat and simmer the juices until almost dry. Pour off the fat and discard. Pour the stock into the pan and deglaze, stirring to scrape up the browned bits, then simmer until reduced to 1/2 cup. Strain the reduced juices and pour over the shredded chicken. Add the parsley, thyme and sumac, and season with salt and pepper. 

Line a 10-by-3-by-3-inch terrine mold with plastic wrap. Pack the chicken mixture into the mold and press overnight in the refrigerator.

Remove the terrine from the mold and slice to the desired thickness. Drizzle with the vinaigrette (recipe below) and serve.

To prepare the vinaigrette, in a large sauté pan over medium-high heat, cook the mushrooms until soft but lightly caramelized, about 4 minutes. Let cool. 

In another sauté pan over very low heat, warm the vegetable oil. Add the shallots and sweat them until soft and translucent, about 3 minutes. Let cool.  

Finely chop the mushrooms and transfer to a bowl. Add the vinegar, olive oil, parsley and shallots with their oil. Season with salt and pepper.