Preheat oven to 350°. Grease and flour an 8" square or round pan. In a large bowl, whisk together flour, turbinado sugar, cocoa powder, baking powder, baking soda, salt, and xanthan gum. Add water, applesauce, oil, and vanilla. Stir well with a whisk until batter is "smooth" looking. Pour into the prepared pan and bake for 50 minutes. Remove from your oven and let cool for 10 minutes. Remove from the pan and let cool on a cooling rack.
This recipe will make about 1 dozen cupcakes. Fill a standard size cupcake pan to about 3/4 full of batter, and bake for about 40 minutes.
Double this recipe for a 9" X 13" cake and bake for 50 minutes.