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Place the butter in a 10" cast iron skillet and place in a cold oven; set the oven to 425°F. The butter will melt and eventually brown as the oven preheats, about 15 to 20 minutes. While this happens, prepare the remaining ingredients.
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In a large bowl, whisk together the flour, cornmeal, sugar, baking powder, salt, and baking soda. In a separate bowl, whisk together the sourdough discard, milk, and eggs until homogenous.
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Once the butter has melted, it will separate, foam, then change from light yellow to golden brown in spots as the milk solids toast. When the butter is golden brown with some darker bits, carefully remove the hot skillet from the oven and set it aside to cool briefly, 2 to 3 minutes.
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Pour most of the butter into the wet ingredients while stirring, leaving a generous tablespoon in the pan to grease the bottom and sides. (Swirl the pan gently so the butter coats the sides.) Once the butter is incorporated, stir the wet ingredients into the dry, mixing until everything is homogenous.
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Transfer the batter into the cast iron pan and spread it into an even layer. Return the pan to the oven.
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Bake the sourdough cornbread for about 15 minutes, until it’s set, golden around the edges, and light brown on top. If, after 15 minutes, the edges are brown but the top remains light, broil briefly until golden brown, about 2 to 3 minutes.
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Remove the cornbread from the oven and allow it to cool in the pan briefly before serving warm or at room temperature. Cornbread is best enjoyed the day it's made.
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Store any leftover sourdough cornbread, well-wrapped, at room temperature for 1 day; freeze for longer storage. Toast leftover slices of cornbread and slather in butter, jam, or honey.
