Here's the cornbread that I made to go along with the bean soup - in fact, I'm eating a piece now as I write this. This is adapted from the Cook's Illustrated people, and I've found this to be one of the better all-cornmeal recipes I've tried (a lot of recipes have half wheat flour and half cornmeal, but some of the other all-cornmeal preps come out with an odd soapy flavor, in my experience.
The quantities below are for an 8-inch (20 cm) cast-iron pan. An old black iron skillet is the traditional cornbread implement, and it's probably not possible to improve on it. I've doubled the recipe, though, and done it in a 9-inch round Calphalon frying pan, which worked fine. A Pyrex dish also works, but doesn't produce as good a crust. Using something that can be heated is key.
So what you want to do is heat an oven to 450F (230C). Take your pan, whatever its material, and put enough oil in it to cover the bottom plus a bit more. Bacon grease is traditional, and cooking a slice or two of bacon in the pan while it's heating up will provide just what you need. Update: At any rate, you want to heat up the pan in the oven while you're getting the batter ready.
While things are heating, take 1/3 of a cup (45 grams) of corn meal and put it in a medium-sized bowl. Then take 2/3 of a cup (90 grams) of corn meal and mix it, in another bowl, with a bit over a teaspoon (5 grams) of granulated sugar, 1/2 teaspoon (3.2 grams) of salt, 1 teaspoon (5 grams) of baking powder, and 1/4 teaspoon (1.25 grams) of baking soda (sodium bicarbonate). Blend these dry ingredients together.
Now bring 1/3 cup of water (just under 80 mL) to a full boil, and add this to the plain corn meal in that first dish. Stir it around to make a homogeneous mush out of it, then add 3/4 cup (about 175 mL) buttermilk to that (regular milk can be substituted; the product will be a bit less assertive). Mix this until homogeneous, then mix in one beaten egg.
Add the dry ingredients from the other bowl and stir to form a batter. Now it's time to get that hot pan out of the oven. Quickly swirl the oil or bacon grease around in it to make sure everything's coated, then pour any excess over into the batter and give it a fast stir, then pour the mixture into the hot pan before anything cools down. Back into the oven it goes for about 20 minutes. If you've doubled the recipe in a larger pan, that'll be 25 minutes, perhaps a bit more.
This should make cornbread that any Southerner would be glad to eat. It's not sweet corn-colored cake, like a Northern corn muffin - those were quite a surprise to me when I first moved up to New Jersey. The hot pan will give it a thin brown crust, and you'll often see these served with that side up on a plate, the way that they fall out of the pan. It is, I can testify, excellent with the bean soup recipe posted earlier today, but will also stand up to almost any soup or stew that you care to throw at it.
Variations are legion; many of them are good. You can add creamed corn to the batter, in which case you'd cut down on the milk. Whole-kernal corn is another classic addition, as are chopped jalapeños. I've seen diced red onion go in there as well. Some shredded cheese will make the whole thing richer. Crumbled bacon (perhaps from the slices you used to grease the pan) is another fine addition, and if you have access to pork cracklings, then you'll be making a variation that I first had in Tennessee over 40 years ago. Enjoy!