Preheat your oven to 400 degrees F.
In a large bowl whisk together the cornmeal, flour, sea salt, baking powder, baking soda, cayenne pepper and black pepper. In a separate bowl, whisk together the buttermilk, granulated sugar and eggs. Add the wet ingredients to the dry and fold the ingredients to combine until completely moistened. Fold in the cheeses, corn kernels and fresh sage. Do not overmix.
In a 10-inch cast iron skillet (or a oven and stove-top safe pan of some kind), melt the butter over medium-low heat. Continue to cook over medium-low heat, swirling the butter with a wooden spoon frequently. Once you start to see brown bits forming on the bottom of the skillet, about 5-6 minutes, remove from heat immediately.
Pour the batter into the skillet with the brown butter. Place in the oven and bake for 20-25 minute or until cooked through and a toothpick comes out clean.
Remove from heat and place on a wire rack to cool slightly. The cornbread is best served warm out of the oven, but will keep for a day or two.