Prepare the cornbread 24–48 hours ahead. Bake the cornbread, allow it to cool completely, then crumble it into large and small pieces. For the best texture, let the crumbled cornbread sit uncovered overnight so it dries out even more.
Preheat the oven to 350°F.
In a large skillet, sauté the chopped celery and onions in a little oil until the celery is tender and the onions are translucent. Set aside to cool slightly.
Place the crumbled cornbread in a large bowl. Drizzle the melted butter over the top and gently fold everything together. From this point forward, continue using a light folding motion instead of stirring to preserve the larger cornbread pieces.
Fold in the sage, poultry seasoning, salt, and black pepper. Taste the mixture and adjust the seasonings if needed before adding the wet ingredients. Allow the salt to be a little less than what you want because there will be salt in the chicken broth.
Gently fold in the milk and eggs until combined, then fold in 1 cup of the chicken broth.
Transfer the dressing to a baking dish. Pour the remaining ¾ cup of chicken broth around the edges of the pan, then gently wiggle the dish so the broth spreads throughout the dressing. Don't press the top smooth—the rough surface creates beautifully toasted edges while baking.
Bake for 45 minutes, or until the top is golden brown and the center is set. Let the dressing cool for several minutes before serving with homemade gravy.