Preheat the oven to 400°F. Put a 10-inch cast-iron skillet in the oven to preheat.
In a large mixing bowl, soak cornmeal in milk for 10 minutes. After 10 minutes, mix in butter and eggs. In a second mixing bowl, whisk together the flour, sugar, baking powder and salt. Add dry ingredients to liquids and mix just until blended. The batter will be lumpy. Stir in the cheese and green chiles.
Remove the skillet from the oven, add 1 tablespoon butter and carefully swirl the butter to coat the bottom and sides of the pan.
Pour the batter in to the hot pan.
Bake for 12 - 15 minutes or until a wooden toothpick inserted in the center comes out clean.