Melt the butter in a 10-inch cast-iron skillet over medium heat until browned but not burned.
Pour the melted butter into a medium bowl and add the milk.
Whisk the milk into the butter.
Add the eggs to the mixture.
In a separate bowl, combine the flour, sugar, cornmeal, baking powder, and kosher salt.
Make a well in the middle of the dry ingredients and pour the butter and milk mixture into it.
Stir everything together with a rubber spatula until just combined.
Let the batter rest for 15 minutes.
Pour the batter into the skillet, smooth the top, sprinkle with sea salt, and bake in the oven.
Bake for 35 to 40 minutes at 350 degrees Fahrenheit, or 25 to 30 minutes if using an 11 ½-inch skillet.
