Preheat oven to 400 degrees, with rack in center of oven. Spray 8-inch square baking dish (preferably pyrex glass or an 8 inch round cast iron skillet) with cooking spray.
Whisk flour, cornmeal, baking powder, baking soda, and salt, and cayenne together in a mixing bowl. Stir in shredded cheese and diced jalapeño.
In a food processor or blender, process brown sugar, corn and buttermilk just until combined, about 5 seconds. Add eggs and process until combined, about 5 more seconds (Lumps of corn will remain).
Using a rubber spatula, fold wet mixture into dry mixture, giving it only a few turns to barely combine (do not overmix). Add melted butter and continue folding until incorporated and just moistened. Pour batter into prepared baking dish and smooth surface with rubber spatula.
Bake until it is a deep golden brown and a toothpick in the center comes out clean, about 25-30 minutes. Let cool 10 minutes, then invert onto a wire rack, turn right side up, and cool another 10 minutes. Serve warm with butter. (Leftovers can be wrapped in aluminum foil and warmed in a 350 degree oven for 10-15 minutes).
Enjoy!