2 cups chicken stock, turkey stock or canned low-sodium broth
Kosher salt and freshly ground pepper
2 pounds brussels sprouts, halved lengthwise
Preheat the oven to 425°. Pour the vegetable oil onto an 11-by-17-inch rimmed baking sheet and heat in the oven. In a large bowl, whisk the cornmeal, flour, sugar, baking powder, salt and baking soda. In another bowl, whisk the buttermilk with the eggs. Pour the buttermilk mixture into the dry ingredients, add the melted butter and stir until blended.
Remove the baking sheet from the oven and swirl to coat with the vegetable oil. Scrape the batter onto the baking sheet and bake for 25 minutes, until the corn bread is springy. Transfer to a rack and let cool. Lower the oven temperature to 375°.
Generously butter two 9-by-13-inch metal baking pans. In a large skillet, melt 2 tablespoons of the butter in 1 tablespoon of the olive oil. Add the celery, carrot and onion and cook over moderate heat, stirring occasionally, until softened, 10 minutes. Add the prosciutto and sage and cook until the prosciutto starts to crisp, about 8 minutes. Stir in 1/2 cup of the white wine; let cool slightly.
Crumble the corn bread into a bowl in small chunks. In another bowl, whisk the eggs with the stock, then pour over the corn bread. Add the prosciutto mixture, season with salt and pepper and toss. Spread the dressing in the prepared baking pans.
Wipe out the skillet and melt the remaining 2 tablespoons of butter and 1 tablespoon of olive oil in it. Add the brussels sprouts and cook over moderate heat, stirring occasionally, until they begin to brown, about 10 minutes. Add the remaining 1/2 cup of white wine and cook for 5 minutes. Season with salt and pepper.
Tuck the brussels sprouts into the dressing. Cover and bake for 20 minutes. Uncover and bake for 10 minutes longer, until crisp on top. Serve hot.