Preheat the oven to 425 F. Grease a regular muffin tin with nonstick spray, or insert paper liners. Set the pan aside.
Combine the dry ingredients in a medium bowl; flour, cornmeal, baking powder, and salt.
In another bowl, stir together the butter, sugar, and oil for a couple minutes.
Add in the eggs, and whisk until combined.
Add in the milk and stir it into the wet ingredients.
Add the dry ingredients to the wet ingredients, and stir them together until combined.
Spoon the batter into 12 muffin cups, filling them evenly, almost to the top of each spot.
Bake the muffins in the preheated oven for 5 minutes.
Keep the muffins in the oven and lower the temperature to 350 degrees. Continue baking the muffins another 8 to 11 minutes, or until a toothpick can be inserted and comes out clean.
Cool the muffins for 5 to 10 minutes in the muffin tin, then remove them and enjoy them warm. Or transfer them to a wire rack to cool completely.