Rye, Kale, Mushroom, and Pumpkin Seed Stuffing

Preheat oven to 350 °. Brush a shallow 3-quart baking dish and a sheet of foil with oil. Place bread in a very large bowl. Toast seeds on a rimmed baking sheet, tossing once, until golden brown, 8 –10 minutes. Let cool; add to bowl with bread. Heat 2 tablespoons oil in a large skillet over medium-high. Add half of mushrooms, season with salt and pepper, and cook, tossing occasionally, until softened, 6 –8 minutes. Transfer to bowl. Repeat with 2 tablespoons oil and remaining mushrooms. Heat 1/4 cup oil in skillet. Add celery and shallots, season with salt and pepper, and cook, stirring often, until shallots are golden brown and soft, 8 –10 minutes. Add kale, sage, and rosemary and cook, tossing often, until kale is wilted, about 2 minutes. Transfer to bowl. Reduce heat to medium and cook wine in skillet, scraping up any browned bits, until almost all evaporated, about 1 minute. Drizzle over bread mixture. Whisk eggs, 2 cups stock, and 1/2 cup oil in a medium bowl; pour over bread mixture. Season with salt and pepper and toss, adding more stock 1/4-cupful at a time as needed (you may not use it all), until combined and bread is hydrated. Transfer to prepared dish and drizzle with oil. Cover with oiled foil; bake until a paring knife inserted into the center comes out hot, 30 –35 minutes. Increase oven temperature to 450 °. Uncover and bake until top is golden brown and crisp, 20 –25 minutes. Let sit 10 minutes before serving. Do ahead: Stuffing can be assembled 1 day ahead. Cover and chill.