Process the corn kernels in a blender until very smooth, about 1 minute. Transfer to a medium saucepan and cook over medium heat, stirring constantly, until thick and deep yellow, about 5 minutes. Remove from heat and set aside.
Carefully add the oil to the hot skillet and continue to bake until oil is just smoking, about 5 minutes. Remove from oven and add butter, carefully swirling pan until butter is melted. Pour all but 1 tablespoon of oil mixture into the cornmeal, leaving remaining oil mixture in pan. Whisk corn purée, beaten eggs, baking powder, baking soda and salt into cornmeal mixture until well-combined.
Pour mixture into the hot skillet and bake until top begins to crack and edges are golden brown, 20 to 22 minutes. Let cornbread cool in pan for 5 minutes. Place a plate over the top of cornbread, then carefully turn over the skillet until the cornbread releases. Then cover cornbread with a serving plate and flip it so it's right-side up. Serve warm.
Variations: Stir in 1/4 cup chopped jalapeños, 3/4 cup shredded Cheddar or pepper jack cheese, or 3 to 4 slices cooked and crumbled bacon just before baking.
Nutrition information per each of 12 servings:
Calories230Fat10 gSodium400 mg