Preheat oven to 400° F. Grease an 8-inch or 9-inch square baking pan. Set aside.
In a large bowl, whisk together flour, cornmeal, granulated sugar, baking powder and salt.
In a separate bowl, whisk together eggs, buttermilk, honey, melted butter and oil. Add the wet ingredients to the dry ingredients, stirring just until combined. Do not over-mix.
Pour batter into prepared baking pan. Bake for 20-22 minutes, or until a toothpick inserted in the center comes out clean. Slice into squares and serve warm.
Notes
Use a finely-ground yellow cornmeal. Coarse cornmeal will give the bread a more grainy (rather than soft) texture.
Let the batter rest for 5-10 minutes before baking, if you have the time. This allows the baking powder to activate and incorporate more air.
Don’t over-mix the batter or it will become too dense, and you'll end up with dry cornbread.
To check if the cornbread is done, insert a toothpick into the center and make sure it comes out clean. Don't cook for too long, or it can dry out.