Heat the oven to 425°F and grease a 9- by 13-inch baking dish. Whisk together the cornmeal, flour, sugar, baking powder, and 2 teaspoons salt in a large bowl. Beat 2 of the eggs in a separate medium bowl, then stir in the oil and milk. Stir the wet ingredients into the dry ingredients just until combined, then transfer the batter to the greased pan. Bake until the cornbread is golden brown and a toothpick inserted into the center comes out clean, 25 to 30 minutes. Cool and let sit at room temperature overnight if time allows.

Heat the oven to 450°F and grease an 11- by 15-inch baking dish (or a 9- by 13-inch baking dish plus a few ramekins). Put the butter in a large skillet over medium heat. When it melts, add the onions and celery and cook, stirring occasionally, until they’re soft, 8 to 10 minutes. Transfer the vegetables to a plate or bowl. If you’re using the sausage, add it to the skillet and cook, stirring occasionally to break up the meat, until no traces of pink remain, about another 10 minutes. Remove with a slotted spoon and drain on paper towels.

Break the cornbread into 1- to 2-inch chunks in a large bowl. Add the onion mixture and the sausage (if you’re using it) along with the seasoned croutons, sage, poultry seasoning, and a few generous dashes of salt and black pepper. Toss to combine, then taste and adjust the seasoning. Beat the remaining 3 eggs and fold them into the cornbread mixture, then gradually add the stock, stirring gently to avoid breaking up the cornbread chunks, until the mixture is moist but not sopping. Transfer the mixture to the greased pan(s). Bake until golden brown, 30 to 40 minutes, and serve hot or warm.