How to Make It
Prepare the Cornbread: Preheat oven to 425°F. Combine self-rising cornmeal mix and, if desired, sugar in a large bowl. Stir together eggs and buttermilk in a medium bowl; add to cornmeal mixture, stirring just until moistened.
Heat salted butter in a 10-inch cast-iron skillet in preheated oven 5 minutes. Stir melted butter into batter. Pour batter into hot skillet.
Bake in preheated oven until Cornbread is golden, about 25 minutes; cool in skillet 20 minutes. Remove from skillet to a wire rack, and cool completely, 20 to 30 more minutes. Crumble Cornbread. Freeze in a large heavy-duty ziplock plastic bag up to 1 month, if desired. Thaw in refrigerator.
Prepare the Dressing: Preheat oven to 350°F. Melt butter in a large skillet over medium-high; add onion and celery, and cook, stirring often, until tender, 10 to 12 minutes. Add sage and thyme, and cook, stirring often, 1 minute.
Stir together eggs in a very large bowl; stir in crumbled Cornbread, onion mixture, stuffing mix, chicken broth, black pepper, and kosher salt until blended.
Spoon mixture into 2 lightly greased 13- x 9-inch (3-quart) baking dishes. Cover and freeze up to 3 months, if desired; thaw in refrigerator 24 hours. (Uncover and let stand at room temperature 30 minutes before baking.)
Bake, uncovered, in preheated oven until lightly browned and cooked through, 1 hour to 1 hour and 15 minutes.
Pecan-Herb Cornbread Dressing: Prepare recipe as directed, increasing fresh thyme to 2 tsp. and adding 2 tsp. chopped fresh rosemary with herbs in Step 4. Stir 1 1/2 cups chopped toasted pecans and 1/2 cup chopped fresh flat-leaf parsley into Cornbread mixture in Step 5; proceed as directed. Garnish with additional chopped parsley.
Cornbread Dressing with Smoked Sausage and Apples: Cook 12 oz. chopped smoked sausage in a large skillet until cooked through; transfer to a paper towel to drain; wipe skillet clean. Prepare recipe as directed, adding 2 large unpeeled Braeburn or Fuji apples, chopped (about 9 oz.), to onion mixture during the last 5 minutes of cook time in Step 4 before adding herbs. Stir sausage into Cornbread mixture in Step 5; proceed as directed.
Make it ahead: All three dressing options can be made a day in advance. Let the cooked dressing cool to room temperature, and then store, covered, in the refrigerator. Reheat before serving.