Step 1

Preheat oven to 250°. Butter a 13x9" baking dish with unsalted butter. Divide 1 medium loaf country-style white bread, torn into irregular 2" pieces (about 10 cups), between 2 large rimmed baking sheets, arranging in a single layer, and bake until dried out, crisp, and barely golden, about 30 minutes. Transfer to a large bowl.

Step 2

Increase oven temperature to 350°. Whisk 2 large eggs and 2 cups low-sodium chicken broth in a large measuring cup or small bowl; set aside.

Step 3

Heat 1 Tbsp. extra-virgin olive oil in a large skillet over medium-high. Cook 1 lb. hot Italian sausage, casings removed, stirring and breaking into small pieces with a wooden spoon, until browned and cooked through, 5–7 minutes. Using a slotted spoon, transfer to bowl with bread, leaving fat behind in the pan.

Step 4

Add remaining 1 Tbsp. extra-virgin olive oil to same pan and reduce heat to medium. Add 4 large onions, thinly sliced, and season generously with kosher salt (at first, it will look like you have way too many onions for the skillet, but they will cook down). Cook onions, stirring occasionally, until deep golden brown and very soft, about 30 minutes.

Step 5

Add 4 celery stalks, thinly sliced, and 3 garlic cloves, thinly sliced, to pan and season with salt and freshly ground black pepper. Cook, stirring occasionally, until celery is slightly softened, 8–10 minutes. Add 2 Tbsp. finely chopped rosemary, 2 Tbsp. finely chopped sage, and 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 in ¼ cup dry white wine and simmer, scraping up any browned bits and stirring often, until liquid is mostly evaporated, about 1 minute.

Step 6

Scrape onion mixture over sausage and bread in bowl and mix well to combine. Pour reserved egg mixture over and fold gently until everything is thoroughly coated; season with salt and pepper. Transfer stuffing to prepared dish and cover tightly with foil.

Step 7

Bake stuffing until bubbling around the edges (peek under the foil to see, then re-cover), 30–35 minutes.

Step 8

Increase oven temperature to 450°. Remove foil from stuffing and bake until heated through and top is browned and crisp, 10–15 minutes.Do ahead: Stuffing can be baked (before crisping) 1 day ahead. Let cool, then chill. Just before serving, uncover and bake at 450° until heated through and crisp, about 15 minutes.