In a medium bowl, whisk together the dry ingredients. In a small bowl, whisk the eggs then add in the buttermilk and cooled (melted) butter, mix until well combined.
Pour the liquid mixture into the dry ingredients and mix until well combined. Set aside.
Place an 8-inch cast-iron skillet over medium-high heat on the stovetop, add the oil and scatter about 1 teaspoon of cornmeal over the oil, do not stir. Allow the cornmeal to cook for about 1 minute (do not get distracted and forget, because it can burn easily). Once the cornmeal starts to turn golden, pour the cornbread batter in and allow to cook for another minute.
Transfer the skillet to the preheated 425°F oven and cook for 25 - 30 minutes or until a knife inserted comes out clean, the top starts to turn golden and you see cracks in the top.
Remove from oven and allow to cool for about 5 - 10 minutes. Lay a plate or serving board upside down over the skillet then carefully flip the skillet and plate over together to invert and remove cornbread. It should come out easily.
You can serve it "upside-down", or flip it back over to serve.
Notes
You can substitute the medium cornmeal for fine cornmeal if you prefer a finer texture cornbread.