Preheat the oven to 450 degrees F. Heat 1 tablespoon butter in a large skillet over medium-high heat until it melts and starts to brown; add the apples, reduce the heat to medium and cook, stirring, until slightly tender, about 4 minutes. Stir in the honey and vinegar, then transfer to a large bowl to cool.
Melt 2 tablespoons butter in the same skillet over medium-low heat. Add the bread cubes and toss to coat, then transfer to one side of a large rimmed baking sheet; add the sausage to the other side. Bake until the sausage is cooked through and the bread is toasted, 8 to 10 minutes. Add the sausage and bread to the bowl with the apples; add the sage, thyme and rosemary.
Heat another 1 tablespoon butter in the skillet over medium heat. Add half each of the leeks, celery and parsnips, and 2 tablespoons water; season with salt and pepper. Cook until the vegetables are translucent, about 8 minutes, then transfer to the bowl with the sausage-apple mixture. Add the remaining leeks, celery and parsnips, and 2 tablespoons water to the skillet, season with salt and pepper and cook about 8 minutes; transfer to the bowl and toss. Warm a spoonful of the stuffing in the skillet with a touch of butter and taste the seasoning; adjust as needed. (It's so important to taste your stuffing while it's hot to get a sense of the seasonings and flavors.) Add the chicken stock to the bowl and toss to moisten all of the ingredients.
Reduce the oven temperature to 350 degrees F. Brush a 9-by-13-inch baking dish with 1 tablespoon butter. Transfer the stuffing mixture to the dish and dot with the remaining 3 tablespoons butter. Cover with aluminum foil and bake 40 minutes, then uncover and continue baking until golden brown, about 40 more minutes.
Photograph by Yunhee Kim
Recipe courtesy Alex Guarnaschelli for Food Network Magazine