Preheat the oven to 400 degrees. Melt 8 tablespoons of butter in a small pot, and let cool.
In a medium bowl whisk the eggs, buttermilk, walnut milk, and slowly stream in the butter.
In a another medium bowl, mix together the flour, cornmeal, sugar, baking powder, and salt.
With a wooden spoon or spatula, make a well in the center of the dry ingredient mix and stream in the liquid, mixing simultaneously. Do not over- mix.
Take the cast iron pan out of the oven, brush it one tablespoon of butter and pour in the batter.
Bake the cornbread for about 20-25 minutes or until firm to touch. Remove from the cornbread from the oven, and let cool completely.