1) Bake the cornbread
Heat the oven to 425°F. Butter an 8-inch square pan or an 8- or 10-inch cast iron skillet.
In a bowl, whisk cornmeal, flour, baking powder, and salt. In a second bowl, whisk eggs, buttermilk, and melted butter. Stir wet into dry just until combined.
Pour into the pan and bake 18 to 22 minutes, until golden and set. A toothpick in the center should come out clean. Cool completely, then crumble. For best dressing texture, let the crumbled cornbread sit out (loosely covered) for a few hours or overnight to dry slightly.
2) Sauté the aromatics
Reduce oven to 350°F. Butter a 9x13-inch dish (or a 12-inch cast iron skillet).
In a skillet over medium heat, melt the butter. Add onion and celery, plus a pinch of salt. Cook 8 to 10 minutes, stirring, until soft and glossy, not browned.
3) Mix the dressing
In a large bowl, combine crumbled cornbread, cooked onion and celery with all the butter, sage, thyme, starting with 1 teaspoon of the salt, pepper, and cayenne if using.
In a small bowl, whisk the eggs with 1 cup of the warm broth. Pour into the cornbread mixture. Add more warm broth, a little at a time, until the mixture is very moist and spoonable. It should mound but not look dry. Plan on 3 to 4 cups broth total, typically 3 to 3 1/2 cups, depending on how dry the cornbread is.
Taste and adjust seasoning (yes, you can). Add the remaining salt only if it needs it, especially if your broth has some attitude.
4) Bake until set and golden
Spoon the mixture into the prepared baking dish and smooth the top. Bake 35 to 45 minutes, until the top is golden and the center is set. If the top browns too fast, loosely cover with foil for the last 10 to 15 minutes.
Doneness check: the center should look set (no liquid pooling) and ideally read 165°F.
Rest 10 minutes before serving. This is when it finishes setting and the slices hold together.
5) Serve
Spoon it up, or cut into squares if you like a clean slice. Finish with chopped parsley if you want a little color. Then go straight for the corner piece. You earned it.