Place a 10" cast iron skillet in the oven, and pre-heat the oven to 400ºF.
Meanhwile, in a large bowl, mix together the cornmeal, flour, baking powder, baking soda, and salt.
In another bowl, add the 6 tablespoon of melted (and slightly cooled) butter and the white and brown sugar. Whisk until creamed.
Whisk in the eggs, then the buttermilk.
Pour the wet ingredients into bowl with the dry ingredients, and stir until just combined. (Do not overmix)
Remove the skillet from the oven, and add 2 tablespoon butter, greasing all of the edges of the pan.
Pour the batter in to the buttered skillet.
Use a spatula or large spoon to level out the top of the batter.
Place the skillet back into the oven, and bake for 20 minutes. Test with a toothpick to make sure it comes out clean. If not, bake for a couple more minutes until done.
Once done, remove from the oven and allow to cool for 5-10 minutes.
Slice into desired pieces, and serve with butter or honey, or on it's own as a side!