In a large bowl, whisk the flour, cornmeal, baking powder, baking soda and salt until combined; set aside.
In a food processor or blender, process the sugar, thawed corn kernels and buttermilk until combined, about 5 seconds. Add the eggs and process until well combined (corn lumps will remain), about 5 seconds longer.
Using a rubber spatula, make a well in the center of the dry ingredients; pour the wet ingredients into the well. Fold the dry ingredients into wet, giving the mixture only a few turns to barely combine; add the melted butter and continue folding until the dry ingredients are just moistened (do not overmix!).
Pour the batter into the prepared baking dish and smooth the surface with a rubber spatula. Bake until deep golden brown and a toothpick inserted in the center comes out clean, 20 to 30 minutes. Cool on a wire rack for 10 minutes, then invert cornbread onto wire rack, turn right side up and continue to cool until just warm, about 10 minutes longer. Cut into squares and serve. Leftovers can be stored, covered, at room temperature for up to 3 days.
To freeze the baked cornbread, cool completely then wrap well in plastic wrap, then in aluminum foil, place in a ziploc freezer bag and freeze for up to 3 months. Allow to thaw in the refrigerator, then remove the foil and plastic wrap, wrap loosely in aluminum foil and reheat in 350-degree oven until warmed through, 20 to 30 minutes.