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Adjust oven rack to middle position; heat oven to 400°F Spray 8-inch square baking dish with nonstick cooking spray. Whisk flour, cornmeal, baking powder, baking soda, and salt in medium bowl; set aside.
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In a food processor or blender, process brown sugar, thawed corn kernels, and buttermilk until combined, aboutp 5 seconds. Add eggs and process until well combined (corn lumps weill remain), about 5 seconds longer.
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Using rubber spatula, make well in center of dry ingredients; our 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, 25-35 minutes. Cool on wire rack 10 minutes; invert cornbread onto wire rack, then turn rightside up and continue to cool until warm, about 10 minutes longer. Cut into pieces and serve.