Preheat the oven: Preheat the oven to 350 degrees F.
Melt the butter: Melt the butter in a large (12-inch) round cast-iron skillet over medium heat. Continue to heat the butter until it’s browned but not burnt (watch it very carefully!). Pour the butter and any brown bits into a medium bowl. Don’t wipe out the skillet; just set it aside.
Combine wet ingredients: Whisk the milk into the butter, then whisk in the eggs until combined. (Don’t add the eggs directly to the hot butter.)
Mix dry ingredients: In a large bowl, whisk together the flour, sugar, cornmeal, baking powder, and kosher salt. Make a well in the middle, pour the butter and milk mixture into the well, and stir with a rubber spatula just until combined. (Don’t worry if it’s a little lumpy.) Set the batter aside for 15 minutes to rest.
Transfer to skillet and bake: Stir the batter, transfer it to the skillet, and smooth the top. Sprinkle generously with flaked sea salt and bake for 25 to 30 minutes, until a toothpick inserted in the center just comes out clean. The top may crack. Cut in wedges and serve warm or at room temperature.
