Steps

1. Bring a large pot of water to a boil. Salt the water and add the onions. Cook for 2 minutes to blanch. Drain and set aside.
2. In a large saucepan with a tight-fitting lid, combine the onions, sugar, and 1 tablespoon of the butter over low heat. Cover and cook until the onions are moist and tender, about 20 minutes. Watch carefully, and shake the pan occasionally to prevent the onions from browning. Drain and set aside.
3. Preheat the oven to 400 degrees.
4. In a large ovenproof skillet, melt the remaining 4 tablespoons butter over moderately high heat. When hot, add the chestnuts and cook, shaking the pan, until the chestnuts are evenly golden (but not deep brown) and are fork-tender, about 10 minutes. Be careful that the chestnuts do not burn. Add the chicken stock and the bouquet garni, and bring to a boil over high heat.
5. Transfer the skillet with the chestnuts to the oven and braise, uncovered, until almost all the liquid has been absorbed, 15 to 20 minutes. Do not allow the chestnuts to dry out. If necessary, spoon the liquid over the chestnuts so that they remain moist.
6. Meanwhile, return the onions to low heat. Stir in the chopped fennel and shallots and cook until softened, about 5 to 10 minutes. Add the walnuts and cook just until heated through.
7. When the chestnuts have absorbed most of the liquid, add the onion mixture. Remove the bouquet garni. Add poultry juices if available, stir, and taste for seasoning.