1. Prepare an ice-water bath. Bring a large pot of salted water to a boil. Add brussels sprouts, and cook until bright green and crisp-tender, about 2 minutes. With a slotted spoon, transfer to ice-water bath. Repeat with green beans and snap peas. Drain.

2. Preheat oven to 375 degrees. Rub inside of pumpkin and cut side of its top with 3 tablespoons oil. Place pumpkin and top on a parchment-lined baking sheet, and roast until they are tender but still holding shape, about 1 hour.

3. Heat 1 tablespoon oil in a large skillet over medium-high heat. Season chicken generously with salt and pepper. Working in batches, cook chicken until golden brown, 3 to 4 minutes per side. Remove excess fat from skillet. Repeat with remaining chicken, adding 1 tablespoon oil to skillet with each batch. Place chicken on a baking sheet. Add stock to skillet, and bring to a boil, scraping bottom. Pour stock into a small bowl.

4. Roast chicken until golden brown and cooked through, about 40 minutes. Reserve pan juices.

5. Heat butter in a large skillet over medium heat. Add apples, and cook, stirring occasionally, until golden and softened, about 10 minutes. Stir in chestnuts, and remove from heat.

6. Combine potatoes, leeks, carrots, turnips, parsnips, squash, and celery root in a large bowl. Toss with remaining 1/2 cup oil, and season with salt and pepper. Spread vegetables in a single layer on a rimmed baking sheet, and roast until golden and tender, about 40 minutes. Add brussels sprouts, green beans, snap peas, apple mixture, and the garlic, and toss. Roast until garlic is golden brown and vegetables are heated through, about 10 minutes.

7. Combine chicken, vegetables, parsley, stock, and 2 tablespoons reserved pan juices in a large bowl. Place mixture in pumpkin, and roast until heated through, about 15 minutes. Slice pumpkin into wedges. Serve each pumpkin wedge with some stew.