Preheat oven to 400 degrees. While the oven preheats, place a 10-inch cast-iron skillet in the oven to preheat at the same time.
In a large mixing bowl, whisk together the flour, cornmeal, sugar, baking powder, and salt.
Add buttermilk, oil, and eggs. Stir to combine just until the dry ingredients are moistened. Do not overmix.
Fold in the green chiles and cheddar cheese.
Remove the preheated skillet from the oven. Coat the pan with enough oil to cover the bottom of the pan, approx. 2 tablespoons. Pour the cornbread batter into the skillet. Bake for 20-25 minutes until a cake tester or toothpick inserted in the middle comes out clean.
Allow the cornbread to cool for 15 minutes before slicing. Store leftovers in an airtight container at room temperature for up to two days.