Heat oven to 450 degrees. Heat 10-inch ovensafe skillet on middle rack for 10 minutes. Place cornmeal on rimmed baking sheet and bake set on lower-middle rack) until fragrant and color begins to deepen, about 5 minutes. Transfer hot cornmeal to large bowl and whisk in buttermilk; set aside.
Add oil to hot skillet and continue to bake until oil is just smoking, about 5 minutes. Remove skillet from oven and add butter, carefully swirl the pan until butter is melted. Pour all but 1 tablespoon oil mixture into cornmeal mixture, leaving remaining fat in pan. Whisk baking powder, baking soda, salt, and eggs into cornmeal mixture.
Pour cornmeal mixture into hot skillet and bake until top begins to crack and sides are golden brown, 12 to 16 minutes. Let cool in pan 5 minutes, then turn out onto wire rack. Serve.