Heat the oven to 350 degrees. Prepare an 8×8-inch or 9×9-inch square baking dish or a 9-inch round cake pan by lining it with parchment paper, greasing it, or coating it with non-stick cooking spray. If using parchment, lightly spraying the pan as well can help. An 8×8-inch baking pan works well for this recipe.
Add the cornmeal, flour, sugar, baking powder, and salt to a large bowl and whisk together. Pour in the melted butter, oil, milk, honey, egg, and egg yolk. Mix gently until the batter is smooth and everything is just incorporated. Avoid excessive mixing so the finished cornbread stays tender.
Leave the batter to rest for 5–10 minutes. This gives the cornmeal time to soften and absorb some of the liquid.
Transfer the batter to the prepared pan. Bake for 24–30 minutes, checking toward the end of the baking time. The cornbread is ready when a toothpick inserted into the center comes out clean. Take care not to bake it longer than necessary.
Let the cornbread cool for about 10 minutes before cutting. Serve it warm with butter, honey, or the honey butter below. For an optional finishing touch, melt 2–3 Tablespoons of butter and brush it over the cornbread immediately after it comes out of the oven.