Preheat oven to 425 degrees. Adjust rack to center. Grease 9 x 9 inch metal pan. Stir cornmeal, flour, baking powder, baking soda, and salt in large bowl. Make a well. Crack eggs into well and stir lightly with wooden spoon, then add buttermilk and milk. Sir wet and dry ingredients quickly until almost combined. Add melted butter, stir until ingredients are just combined. Pour batter into greased pan. Bake until top is golden brown and lightly cracked and edges have pulled away from side of pan, about 25 minutes. Transfer pan to wire rack, cool 5 to 10 minutes. Cut into squares.
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