1 tablespoon extra-virgin olive oil
1 pound sweet Italian sausage, casing removed
6 tablespoons unsalted butter, divided, plus more for dish
1 yellow onion, chopped (about 1 1/2 cups)
1 cup roasted, shelled chestnuts, coarsely chopped
2 cups assorted mushrooms, such as shitake, baby bello, white, oyster, stems removed
4 large eggs, beaten
2 1/2 cups low-salt chicken broth
2 teaspoons kosher salt
1 1/2 teaspoons freshly ground black pepper
Preheat oven to 350°F. Scatter bread on a rimmed baking sheet. Toast until golden brown, tossing once, about 15 minutes. Let cool completely. Bread can be toasted 1 day ahead. Store airtight at room temperature.
Heat oil in a large skillet over medium heat. Add sausage and cook, breaking up into small pieces with the back of a spoon, until browned and cooked through, 8-10 minutes. Drain on a paper towellined plate; let cool. Melt 2 tablespoons butter in the same skillet over medium-low heat. Add onion and chestnuts and cook, stirring occasionally, until soft, 1012 minutes. Can be made one day ahead. Let cool; cover and chill.
Prepare mushrooms: slice all mushrooms and sauté over medium heat in skillet for 7-9 minutes with 2 tablespoons butter.
Preheat oven to 350°F. Butter a 3-quart shallow baking dish. Whisk eggs to blend in a large bowl; whisk in broth. Stir in sausage, the onion-chestnut mixture, mushrooms, salt and pepper. Add bread; toss until evenly distributed and bread has absorbed the liquid. Transfer to prepared dish; dot with remaining 2 tablespoons butter.
Bake until stuffing is hot and the top is golden brown, about 40 minutes