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Preheat oven to 400 degrees (if not already on from making the Cornish Hens.)
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Mix milk and vinegar in a measuring cup. Let stand for a few minutes while you prepare the dry ingredients.
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Melt 4 tablespoons butter in a small bowl in the microwave. Then let sit out to cool slightly.
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In a large mixing bowl, mix together cornmeal, flour, maple sugar, baking powder, baking soda, and salt.
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In a medium mixing bowl, mix together the milk and vinegar mixture and the eggs.
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Wait until you have 30 minutes left on the Cornish hens’ bake time to continue, if you’d like both to be done around the same time. (Otherwise go ahead, the cornbread will be a good snack while you’re waiting for the hens to finish cooking.)
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Add the 4 tablespoons melted butter to the mixing bowl with the wet ingredients and stir to mix. Pour wet ingredients into dry ingredients and stir until combined. Do not overmix. It’s okay if there are still some streaks of flour or cornmeal.
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Heat a 10 inch cast iron skillet over medium heat. Melt remaining 1 tablespoon butter in the skillet, and turn so butter coats the entire bottom of the skillet. Carefully pour batter into the skillet. Turn off stove and transfer skillet to oven. Bake 17-20 minutes, until a toothpick inserted into the center comes out clean. While cornbread is baking, make the maple butter.