Adjust oven rack to middle position; heat oven to 400 degrees. Spray 8-inch-square baking dish with nonstick cooking spray. Whisk flour, cornmeal, baking powder, baking soda, and salt in medium bowl until combined; set aside.
In food processor or blender, process brown sugar, thawed corn kernels, and buttermilk 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 dry ingredients; pour wet ingredients into well. Begin folding dry ingredients into wet, giving mixture only a few turns to barely combine.
Add melted butter and continue folding until dry ingredients are just moistened.
Pour batter into prepared baking dish; smooth surface with rubber spatula.
Bake until deep golden brown and toothpick inserted in center comes out clean, 25 to 35 minutes.
Cool on wire rack 10 minutes; invert cornbread onto wire rack, then turn right side up and continue to cool until warm, about 10 minutes longer.
Cut into pieces and serve.