1. Cut a slit in each chestnut with scissors or a paring knife. Cook chestnuts in a pot of boiling water for 20 minutes, then drain in a colander. When cool enough to handle, peel off and discard shells and inner brown skins.

2. Heat 3 tablespoons olive oil in a large saute pan over medium high until shimmering. Saute chestnuts, stirring occasionally, until they begin to brown. With a slotted spoon, transfer chestnuts to a plate. Add both mushrooms to skillet and saute, stirring occasionally, until mushrooms release their juices and begin to turn golden, about 15 minutes. Transfer to a large bowl and season with salt. Add bread cubes, and toss to mix.

3. Heat 3 tablespoons olive oil in same pan over medium high. Add carrots, onions, celery, sweet potato, and garlic; season with salt and pepper. Cook, stirring occasionally, until vegetables begin to brown, about 10 minutes. Add stock and simmer until vegetables are tender, about 5 minutes. Transfer contents of pan to bread mixture along with the chestnuts. Add apples, herbs, and another 3 tablespoons olive oil. Toss well and season stuffing with salt and pepper, then mix in the eggs.

4. Preheat oven to 375 degrees. Remove top of pumpkin by cutting a circle about 5 inches in diameter around stem with a paring knife: reserve top. Scrape out and discard seeds and stringy flesh from pumpkin. Rub inside of pumpkin with remaining 1 tablespoon olive oil and season with salt and pepper. Spoon stuffing into pumpkin and replace top. Bake stuffed pumpkin on a rimmed baking sheet until pumpkin is tender when pierced with a skewer, 1 1/2 to 2 hours. (Do not overcook pumpkin or the side may split.) To serve, remove top and scoop out stuffing and some pumpkin flesh with a large spoon.