Preheat the oven to 425°. Warm a 10-inch cast-iron skillet over moderate heat. Add the vegetable oil and heat.
Meanwhile, in a bowl, sift the flour with the sugar, baking powder and salt. Stir in the cornmeal. Add the milk and eggs and stir lightly. Add the melted butter and stir just until blended.
Scrape the batter into the hot skillet; the oil should sizzle. Transfer the skillet to the oven and bake the corn bread for about 25 minutes, or until the center springs back when gently pressed. Turn the corn bread out onto a rack to cool. (This will yield 3 pounds of corn bread.)
Reduce the oven temperature to 375°. In a large saucepan, cook the chorizo over moderate heat until the edges are crisp, about 6 minutes. Add the butter and let it melt. Add the onions, celery and carrot and cook until the onions are translucent, about 12 minutes. Add the garlic, thyme, sage and rosemary and cook until fragrant, about 1 minute. Transfer the chorizo mixture to a large bowl.
Cut the corn bread into 1-inch pieces. Spread it on a rimmed baking dish and toast for about 20 minutes, stirring once, until golden in spots. Add the corn bread to the chorizo. Add the chicken stock, eggs, salt and pepper and toss gently until evenly coated. Transfer the stuffing to a 10-by-14-inch baking dish. Bake in the top third of the oven for about 40 minutes, until golden on top. Serve warm.
The baked stuffing can be refrigerated overnight. Bring to room temperature before reheating.
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