Heat a large skillet over medium heat and cook the chorizo, breaking it up with a spoon and stirring occasionally as it cooks, until it begins to brown, about 5 minutes. Add the onion, carrot, celery and garlic to the chorizo and cook, stirring occasionally, until the vegetables have browned, about 10 minutes. Add the crumbled cornbread and cilantro and gradually pour in enough of the stock so the stuffing is not too dry but at the same time not too wet. Stir gently and well.
Butter a small casserole dish. Spread the stuffing in an even layer. Bake until it's heated through and lightly browned on top, about 20 minutes. Serve right away, garnished with the cilantro and cotija, if desired.