Preheat oven to 425 degrees. Place an 8-inch cast iron skillet in the oven to preheat.
Combine the butter, milk cornmeal and brown sugar in a small saucepan. Bring to a slow, steady simmer and whisk for a few minutes until thickened.
Add eggs, baking powder and salt to a medium bowl and whisk lightly. Add cornmeal mixture and stir until well combined.
Oil cast iron skillet and pour in batter. Bake for 20-25 minutes, until cornbread is golden around the edges and cooked through.