Place a rack in middle of oven; preheat to 250°. Arrange bread in a single layer on a rimmed baking sheet. Bake, tossing occasionally, until dried out, about 1 hour. Let cool; transfer to a very large bowl. Increase oven temperature to 350°.
Meanwhile, heat oil in a large skillet over medium-high. Cook onions, fennel, and celery, stirring often, until softened but not yet browned, 8–10 minutes. Add wine and cook, stirring, until almost completely evaporated, about 1 minute. Add butter and cook, stirring, until melted, about 3 minutes. Scrape vegetable mixture over bread in bowl and mix in parsley, sage, rosemary, thyme, salt, and pepper.
Whisk eggs and broth in a medium bowl to combine.
Pour over bread mixture; fold gently until thoroughly coated.
Put stuffing mixture into a 13x9" baking dish and pack stuffing down.
Cover with foil and bake until you can see some bubbles around the edges of the dishes, 30–35 minutes.
Increase oven temperature to 425°. Uncover stuffing and bake until top is golden brown and crisp, 20–25 minutes. Let sit 10 minutes before serving.