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Preheat oven to 425°F with rack in middle. Heat a well-seasoned 10-inch cast-iron skillet in oven 10 minutes.
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Stir together cornmeal, flour, sugar, baking soda, and salt. In another bowl, whisk together eggs, buttermilk, and tomatoes.
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Remove skillet from oven (handle will be very hot) and add butter, swirling gently to coat bottom and sides. Whisk melted butter into buttermilk mixture. Stir cornmeal mixture into buttermilk mixture just until smooth.
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Pour batter into skillet. Bake until golden, 20 to 30 minutes. Invert skillet over a platter to unmold corn bread. Cool 5 minutes. Serve warm.