Adjust oven rack to middle position and heat oven to 400 degrees. Spray 8-inch square baking dish with vegetable oil spray. Whisk flour, cornmeal, baking powder, baking soda, and salt in medium bowl until combined; set aside.
Process buttermilk, corn kernels, and brown sugar in food processor or blender until combined, about 5 seconds. Add eggs and process until well combined (corn lumps will remain), about 5 seconds longer.
Using rubber spatula, make well in center of flour mixture; pour buttermilk mixture into well.
Begin folding dry ingredients into wet, giving mixture only a few turns to barely combine. Add melted butter and continue to fold until dry ingredients are just moistened. Transfer batter to prepared baking dish and smooth top with rubber spatula.
Bake until cornbread is deep golden brown and toothpick inserted in center comes out clean, 25 to 35 minutes, rotating dish halfway through baking. Let cornbread cool in pan on wire rack for 10 minutes.
Remove cornbread from pan and let cool on wire rack for 10 minutes longer before serving. (Leftover cornbread can be wrapped in aluminum foil and stored at room temperature for 24 hours. Reheat cornbread in 350-degree oven for 10 to 15 minutes.)