Preheat oven to 400 degrees.
Put cast iron skillet in oven also to heat up.
In a large bowl, beat the 2 eggs together.
Add the milk and the melted butter and whisk.
In a smaller bowl, mix the dry ingredients together (cornmeal, sugar, xanthan gum, baking powder, rice flour and salt).
Add dry ingredients to wet mixture and stir until well combined.
Let it rest for a couple of minutes to set up.
Add shredded cheese to wet mixture.
Remove skillet from oven carefully, and swirl a little butter around pan to coat.
Pour batter into pan.
Bake in oven for 15-20 minutes.
Serve while still warm.
I also baked some of the cornbread in small canning jars.