Put he flour, cornmeal, sugar, baking powder, baking soda, and salt in a mixing bowl. Whisk to combine.

In a separate bowl, add the buttermilk, eggs, and cooled melted butter. Whisk well.

Add the liquid to the dry ingredients and stir until just combined. Stir in the cheese.

In a heavy skillet, preferably cast iron, melt some butter or heat some oil over medium heat.

Pour the batter into the skillet and cook until it bubbles up. Carefully flip, and continue cooking until both sides are golden brown.

Continue cooking until all are done. Serve with desired accompaniments.