Preheat oven to 450 degrees F (230 degrees C).
Pour vegetable oil into a 10-inch cast-iron skillet and swirl oil to coat bottom and sides of skillet. Place skillet into preheated oven until very hot, 3 to 5 minutes. Remove skillet from oven.
Whisk cornmeal, flour, sugar, baking powder, baking soda, and salt in a bowl. Beat eggs in a separate bowl and stir buttermilk into eggs. Pour half (2 tablespoons) of vegetable oil from the hot skillet into buttermilk mixture, retaining remaining oil in skillet, and beat until oil is incorporated. Mix buttermilk mixture into dry ingredients to make a smooth batter. Pour batter into skillet.
Bake in the oven until top is golden brown, 18 to 20 minutes. Cut cornbread into servings while in skillet; serve warm.
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