Preheat the oven to 400F and adjust the rack to the middle position. Grease an 8x8 glass baking dish with butter.
Add the flour, cornmeal, baking powder, baking soda, and salt to a medium bowl. Whisk well to combine.
Add the buttermilk, corn kernels, and brown sugar to a blender or food processor and process for 5 seconds, or until the corn is broken down. Add the eggs and process for an additional 5 seconds.
Add the buttermilk to a glass measuring cup or small glass bowl. Add the sourdough discard and whisk gently until the two are combined and uniform.
Make a well in the center of the dry ingredients and add the buttermilk and sourdough discard mixture. Use a silicone spatula to fold the dry ingredients into the center of the well. Fold just until the dry ingredients are moistened, but still slightly dry.
Add the melted butter to the batter and fold it in with a few turns, just until the batter is slightly less try. You still want streaks of melted butter, so the goal is to incorporate without making the mixture uniform. This will give it that classic rustic cornbread texture.
Pour the batter into the prepared baking dish and bake in the preheated oven for 35 minutes, or until a cake tester inserted in the middle comes out clean.
Remove the pan from the oven and let cool for 10-15 minutes before slicing and serving.