Preheat the oven to 350 degrees F (175 degrees C). Grease a 9x9-inch baking dish.

Mix together cornmeal, flour, baking powder, sugar, and salt in a bowl. Sift 3 times. Stir in beaten eggs and milk until well combined. Set aside.

Place butter in the prepared baking dish and melt in the preheated oven. Pour hot, melted butter into cornmeal mixture and mix until incorporated. Transfer batter to the prepared baking dish.

Bake on the center rack in the preheated oven until the edges of cornbread pull away from the sides of the dish and a toothpick inserted into the center comes out clean, 30 to 35 minutes. Let cool for 10 minutes before cutting.