Combine buttermilk, corn flour, and cornmeal in a medium bowl and stir until completely moistened. Cover and refrigerate 4 hours or overnight. (This helps soften the grains and improves the moisture and texture of the cornbread.) Remove buttermilk mixture from fridge and let come to room temperature before using.

Preheat oven to 400 °F. Butter an 8x8-inch square baking pan. Line with parchment paper and butter the parchment.

In a medium mixing bowl, whisk/sift the all-purpose flour, baking powder, and salt together. Set aside.

In a large mixing bowl, whisk together the melted butter, oil, brown sugar, honey, and eggs until thoroughly combined.

Add buttermilk mixture to the bowl and whisk until incorporated. Stir in the flour mixture until no pockets of flour remain.

Spread batter into prepared pan and bake 28-30 minutes, or until golden brown and toothpick comes out clean. Rotate halfway through baking time if needed for even browning.

Remove from oven and immediately brush with 1-2 tablespoons honey.

Serve warm or room temperature with salted butter and honey.