Preheat your oven to 350°F. Grease the inside of a large casserole dish with unsalted butter, making sure to coat all sides to prevent sticking. Set the greased dish aside for use later.
Place a large nonstick skillet over medium-high heat. Add the Mexican chorizo and crumble it with a spatula. Cook until the chorizo is browned and fully cooked, which should take about 5 minutes. Once browned, you can use a slotted spoon to transfer the chorizo to a plate if you want to remove some fat, but keep it in the skillet for the next step if you like it extra flavorful. I usually keep it all in for maximum taste!
To the browned chorizo (from Step 2), add the finely diced onion, chopped celery, minced garlic, chopped sage leaves, chopped rosemary, and chopped thyme leaves. Cook over medium-high heat, stirring occasionally, for about 10 minutes until the vegetables are fragrant and begin to soften. Remove the skillet from heat when finished.
In a medium bowl, combine the chicken stock and large egg. Whisk well until the mixture is fully combined and smooth. This will help bind the stuffing and keep it moist during baking.
Add the coarse cornbread pieces and the chorizo-vegetable mixture (from Step 3) to the prepared, greased casserole dish (from Step 1). Gently toss everything together to evenly distribute the ingredients without breaking up the cornbread too much.
Pour the chicken stock and egg mixture (from Step 4) evenly over the cornbread stuffing in the dish, ensuring it soaks through all the layers. Place the casserole dish in the preheated oven and bake for 25 minutes, or until the top is golden and the center is cooked through. For an extra boost of flavor, I sometimes sprinkle a bit more fresh herbs on top before serving!