1. Preheat your oven to 375 degrees Fahrenheit (190°C). While the oven is preheating, place a 9-inch cast-iron skillet in the oven to preheat as well if you're using one. If you're using a Pyrex dish, there's no need to preheat it.
2. In a mixing bowl, combine the cornmeal, all-purpose flour, baking powder, and salt. Mix these dry ingredients together until well combined.
3. In a separate bowl, beat the egg and then add the buttermilk, 2 tablespoons of oil, and the milk. Mix these wet ingredients until they are well combined.
4. In a small bowl or cup, dissolve the baking soda in a little bit of warm water, and then add it to the wet ingredients mixture. Stir to combine.
5. Slowly pour the wet mixture into the dry mixture, and stir until just combined. Be careful not to overmix; a few lumps are okay.
6. If you're using a preheated cast-iron skillet, carefully remove it from the oven (remember to use oven mitts), and either grease it with a little oil or use non-stick cooking spray. Pour the cornbread batter into the skillet. If you're using a Pyrex dish, simply pour the batter into the dish.
7. Place the skillet or Pyrex dish in the preheated oven.
8. Bake for 35-40 minutes, or until the cornbread is golden brown on top and a toothpick inserted into the center comes out clean.
9. Once done, remove the cornbread from the oven using oven mitts, and let it cool for a few minutes.
10. Slice and serve your Southern Cornbread while it's still warm. It's perfect as a side dish for soups, stews, or as a tasty snack on its own. Enjoy!