Rinse and dry the blueberries. If using frozen blueberries, see note.
Preheat the oven to 400°F and place a rack in the middle of the oven.
Grease a 9"x13" cake pan and insert a 13"x18" sheet of parchment so that the bottom and the two 13" sides of the cake pan are covered (the two 9" sides will still be exposed). Crease the paper along the bottom edges of the 13" sides of the pan and also fold and crease the 13" ends of the parchment so that the flaps overhang the outsie of the pan.
Melt the butter gently over low heat, turning off the heat just before the butter has completely melted. The residual heat will melt the rest of the butter.
Add the cornmeal, flour, 1 cup of sugar, baking soda, baking powder, and salt into a large bowl and whisk to combine.
Add the buttermilk and eggs to a medium bowl and whisk to combine. Drizzle in the butter slowly and whisk to combine.
Make a well in the dry ingredients and add the liquid. Combine with a fork just until the dry ingredients have been completely incorporated into the liquid. The texture should be moist and gloppy, not liquid.
Add 2/3 of the batter to the cake pan and spread into a roughly even height, pressing into the corners. Sprinkle in half of the blueberries and distribute them evenly. Add the rest of the batter on top and spread to cover. Add the rest of the blueberries, distributing them evenly, and press down on the berries until they're just covered by the batter.
Bake for approximately 25-30 minutes until a toothpick inserted comes out clean. Take care to note that the top third is done; if the toothpick comes out clean but the top is still jiggling when you move the pan, give it a few more minutes.
Remove the pan from the oven and let rest for about 10 minutes. Run a butter knife along the edges of the cornbread that are touching the 9" sides of the pan to loosen the cornbread. Lift the cornbread using the parchment handles and move to a cooling rack. Remove the parchment from the bottom; if you can't slide it out easily, place a baking sheet on the top of the cornbread and carefully flip the sheet, cornbread, and cooling rack over, then take off the cooling rack and remove the parchment, then replace the cooling rack and flip the cornbread over again and remove the sheet.