Preheat oven to 375 degrees F. In a small skillet, melt butter over medium heat. After butter has melted, let continue to cook, stirring frequently, until butter has browned, about 3 minutes. Transfer to cake pan. In a small bowl, whisk together eggs and milk. In a large bowl, whisk together cornmeal, flour, sugar, baking powder, and salt. Stir in egg mixture until combined. Pour batter into pan and smooth out the top. Bake until golden and a cake tester comes out clean, about 25 minutes.
