Preheat oven to 475°F (245°C). Grease an 8-inch square baking pan with butter.
In a medium bowl, whisk together flour, cornmeal, baking powder and salt.
Stir in sugar until well combined. Mix melted unsalted butter into the dry ingredients alternately with milk while continuously mixing at low speed (using an electric mixer).
Add eggs one by one, beating for about 30 seconds after each addition.
Bake in preheated oven until tops are golden and a tester inserted into the center of loaf comes out clean, about 25 minutes.