Heat 10" cast iron skillet (or cast iron pie dish) over medium heat for 2 minutes. Add one tablespoon of butter to the skillet and swirl to coat as the butter melts. The butter should sizzle, but not brown. Immediately place the onion slices in hot butter in the skillet in a single layer. You can crowd them a bit because they will shrink as the cook.
Fry onions for about 2-3 minutes, or until golden. Using a spatula, carefully turn onion slices over to fry the other side. When onions are nicely browned on each side, carefully remove them from skillet using a spatula and set aside on a plate.
Assembling Casserole
Melt 1 tablespoon butter in a 10" cast iron pie dish (or cast iron skillet). Swirl melted butter to coat bottom and sides.
Cornbread Layer #1 • Cubed Into the prepared cast iron pie dish, lay in 1 ½ - 2 cups of sliced (or crumbled) leftover cornbread, so that the bottom of the dish is completely covered by about ½ inch of cornbread.
In a small bowl, whisk together 2 eggs and ⅓ cup milk. Season with ¼ teaspoon salt and a few turns of freshly ground pepper. Pour evenly over cornbread layer in pie dish. Press down slightly, just enough to flatten layer.
Grated Cheese LayerSprinkle grated cheese over cornbread layer.
"Leftover" LayerSpread leftover chili (or stew, or whatever you are using) on top of the grated cheese.
Cornbread Layer #2 • Crumbled Spread 1 ½ - 2 cups crumbled leftover cornbread over the top of the Leftover layer.
Carefully crack 6 to 8 eggs onto casserole, arranging them evenly in a ring.
Arrange pan-fried onions around egg yolks. This is actually kind of fun: I was thinking of Vincent Van Gogh's "Starry Night" while I was working.
Bake for 30 to 35 minutes at 350°. Eggs whites should be set, and the whole thing is relatively firm to the touch. Allow casserole to rest for 10 minutes before slicing.
Garnish with chopped fresh parsley or cilantro. Serve warm.
Notes
For best results, use leftover cornbread from my Sweet Skillet Cornbread recipe. Preparing Leftover CornbreadIf possible, try to avoid making your leftover cornbread into fine breadcrumbs. This will result in a very heavy, dense casserole. I prefer to cube, or even slice, the cornbread that I use for the first layer. I try to slice it ⅜ - ½" thick, and use the slices to cover the bottom of the pan. That said, occasionally leftover cornbread defies slicing; in which case I try to keep it in the largest crumbled state possible. I use the larger crumbles for the first layer, and smaller crumbles for the top layer. CheeseCheddar and Mozzarella are always safe bets, but feel free to use whatever goes well with your "leftover layer."