In a medium bowl, stir together the cornmeal, flour, granulated sugar, baking powder, baking soda, and kosher salt. Whisk in the eggs and milk until a smooth dough forms.
Place the butter (cut into pieces) in a 9 or 10-inch cast iron skillet or other oven-safe skillet. Place it in the oven until the butter melts, about 5 minutes.
Carefully remove the skillet with a hot pad. Brush the melted butter up the sides of the pan. Then pour it into the batter and stir until fully combined. Pour the dough back into the preheated pan.
Bake 20 minutes, until puffed and a toothpick comes out clean. Allow to cool for a few minutes, then slice into pieces and serve.