Preheat oven to 375F.
In a large bowl, mix together gluten free flour blend, xanthan gum (if using), cocoa powder, brown sugar, granulated sugar, and baking soda.
Then, add in egg, vanilla extract, milk and vegetable oil. Whisk until smooth.
Coat a donut pan with 12 donut wells with nonstick cooking spray (make sure it does not have flour in it if you need to be gluten-free).
Spoon batter into the donut pan. The batter should just about reach the top of the pan. Bake at 375F for 10 minutes or until the donuts spring back when you touch them. Cool on a wire rack.
To make the frosting, in a small pot over medium-low heat, whisk together milk and white chocolate chips until melted.
Add in vanilla and powdered sugar and whisk until the sugar is melted and the frosting is smooth.
Take off the heat to thicken slightly.
When the donuts are cooled, dip them into the frosting and shake off any excess.
Place back on wire rack and sprinkle candy cane bits over the donuts. Repeat until you have completed all of the donuts.