Preheat the oven to 250°. Butter a 13 x 9-inch baking dish with Butter without salt. Divide 1 loaf medium white country bread, torn into irregular 2″ pieces (about 10 cups), between 2 large rimmed baking sheets, arranged in a single layer, and bake until dry, crisp and barely golden, about 30 minutes. Transfer to a large bowl.
Increase the oven temperature to 350°. Whip 2 large eggs and 2 cups low sodium chicken broth in a large measuring cup or small bowl; put aside.
Heat 1 tbsp. extra virgin olive oil in a large skillet over medium-high heat. To cook 1 lb hot Italian sausage, casings removed, stirring and breaking into small pieces with a wooden spoon, until browned and cooked through, 5 to 7 minutes. Using a slotted spoon, transfer to a bowl with the bread, leaving the fat in the pan.
Add the rest 1 tbsp. extra virgin olive oil in the same skillet and reduce the heat to medium. To add 4 large onions, thinly slicedand season generously with kosher salt (at first it looks like you have way too many onions for the pan, but they will cook). Cook onions, stirring occasionally, until golden brown and very tender, about 30 minutes.
To add 4 celery stalks, thinly slicedand 3 garlic cloves, thinly slicedfry and season with salt and freshly ground black pepper. Cook, stirring occasionally, until celery is slightly softened, 8 to 10 minutes. To add 2 tbsp. finely chopped rosemary, 2 tbsp. finely chopped sageand ½ cup (1 stick) unsalted butter, cut into pieces, and cook, stirring occasionally, until butter is melted and mixture is combined, about 3 minutes. Pour ¼ cup dry white wine and simmer, scraping up browned bits and stirring often, until most of the liquid has evaporated, about 1 minute.
Scrape the onion mixture over the sausages and bread in a bowl and toss well to combine. Pour reserved egg mixture over top and fold gently until well coated; Season with salt and pepper. Transfer stuffing to prepared dish and cover tightly with foil.
Bake stuffing until bubbly around edges (peek under foil to see, then cover), 30 to 35 minutes.
Raise the oven temperature to 450°. Remove foil from stuffing and bake until heated through and top is golden brown and crispy, 10 to 15 minutes.
Do it in advance: The stuffing can be cooked (before being crispy) 1 day in advance. Leave to cool, then refrigerate. Just before serving, uncover and bake at 450°C until hot and crispy, about 15 minutes.