Arrange oven rack in the middle of the oven. Preheat oven to 450 degrees.
Place 2 Tablespoons of butter in the bottom of a 9x9 inch baking pan or large cast iron skillet and place in the oven to melt. Once melted, remove from the oven and swirl the butter around to coat.
In a large bowl, whisk together the cornmeal, flour, sugar, baking powder, baking soda, and salt.
In a medium bowl, whisk the eggs until frothy. Whisk in the milk and buttermilk until combined.
Pour the egg mixture into the flour mixture. Mix just until dry pieces are incorporated. Do not overmix.
Fold in the remaining stick of melted butter. Allow mixture to sit for 5 minutes.
Bake 15-20 minutes, until knife inserted into center comes out clean.
Serve warm cornbread with butter, honey, and syrup as desired.
NOTE: This recipe makes 9 squares of cornbread. You can double the recipe and use a 9x9 inch baking pan. To freeze, allow the cornbread to cool completely. Then, remove the bread from the pan and wrap tightly in plastic wrap and a layer of foil. Freeze for up to 3 months, thaw in the refrigerator or on the counter overnight before serving.