Preheat oven to 375°F. Grease a 9x13-inch baking pan with butter.
In a large skillet, melt the butter over medium heat. Add in the onion and celery. Cook until softened, about 5 minutes. Add in the garlic, sage, parsley, and thyme. Cook until fragrant, 1-2 minutes.
3 tablespoons unsalted butter, 2 onions, 3 ribs celery, 2 cloves garlic, 2 tablespoons minced fresh sage, 2 tablespoons minced fresh parsley, 1 tablespoons minced fresh thyme
Remove from the heat and pour into a large bowl.
To the vegetables, add the cornbread, egg, chicken broth, milk, brown sugar, salt and pepper. Gently stir until combined.
9 cups cubed cornbread, 1 large egg, 1 cup low-sodium chicken broth, ¾ cup whole milk, ¼ cup brown sugar, ¼ teaspoon ground black pepper, 1 teaspoon kosher salt
Spoon the mixture into your prepared pan. Cover with foil and bake for 30 minutes. Remove the foil and bake for another 20 minutes or until the top is golden.