How to Make It
In a large pot, combine the stock, chicken, celery, onion, chopped carrot, garlic, peppercorns and thyme sprigs and bring to a simmer over moderately high heat. Reduce the heat to low and simmer, turning the chicken once, until it is cooked through, about 1 1/2 hours. Transfer the chicken to a platter; let cool.
Strain the broth and return it to the pot. Boil the broth over high heat, skimming occasionally, until reduced to 6 cups, about 12 minutes. Cover the broth and keep it hot. Remove the meat from the chicken and tear it into large pieces.
In a small saucepan of boiling water, cook the baby carrots until tender, about 5 minutes; using a slotted spoon, transfer them to a plate. Repeat with the turnips, cooking them for 4 minutes, and the peas, cooking them for 1 minute.
In a large skillet, combine the chicken, baby carrots and 1 cup of the broth. Cover and rewarm gently, then remove from the heat. Stir the mustard into the remaining broth and season with salt and pepper. Spoon the chicken and vegetables, including the raw zucchini, into large shallow bowls. Sprinkle the chopped thyme and sliced shallot over the top, then ladle in enough hot broth to cover. Add 2 pieces of the Comté Polenta to each bowl and serve.