Preheat the oven to 350ºF (180ºC).
Add a swirl of olive oil to a deep skillet. Heat over medium-high flame until shimmering. Add the ground sausage, and cook, stirring occasionally to break up any large pieces of meat, until browned all over. Spoon the sausage into a bowl, and set aside.
Reduce the flame to medium. Add another swirl of oil to the pan if it seems dry. Add the onions, celery, and carrots to the pan. Season with salt and pepper. Sauté until slightly softened, and onions are golden, 3 to 4 minutes.
Pour in the wine, using a spoon to scrape up any browned bits in the pan. Cook for 1 minute.
Add the apple and chestnuts. Stir in the lemon thyme and fennel. Cook for 1 to 2 minutes, until apple is slightly softened & fragrant. Remove from burner, and set aside while you pull the rest of the stuffing together.
Add the eggs and broth to a deep bowl. Beat lightly to mix.
Add the bread cubes, and the sausage, onions, celery, carrots, apples & chestnut mixture.
Stir until bread is fully coated, and liquid has been mostly absorbed.
Grease the bottom and sides of a 9-inch by 13-inch (22-cm by 33-cm) deep roasting pan. Spoon the stuffing into the pan, patting it down into place. Cover tightly with foil. At this point you can set in the fridge overnight before baking. It’ll give the bread time to absorb the flavors, but if pressed for time, you can go straight to the next step (see Note).
Bake 30 minutes. Remove the foil, and bake for 30 to 40 minutes more, until the stuffing is deeply golden. Serve hot.