Make the Icing: Stir together the powdered sugar, milk, and vanilla extract in a small bowl. It should flow easily from a fork. Adjust with additional powdered sugar (to thicken) or additional milk (to thin) as needed. Set aside.
Make the Swirl: In a small bowl, combine dark brown sugar, butter, and ground cinnamon. Mix until a thick paste forms. Add milk. Stir to combine. Mixture will be thick and look curdled. This is normal. As long as it's thoroughly combined, you're fine. Transfer mixture to a pastry bag fitted with a small (number 4) tip or, if you don't have a tip, cut a hole in the bag later. Set aside.
Make the Waffle Batter: In medium mixing bowl, whisk together white rice flour, cornstarch, sweet rice flour, baking powder, granulated sugar, salt, and xanthan gum. Add the milk, eggs, oil, and vanilla extract. Whisk until smooth.
Heat waffle iron according to manufacturer's directions. Spray iron generously with non-stick cooking spray. Spoon batter onto hot iron (amount of batter will vary depending on your iron). Cook until crisp. Serve with icing. (Note: to clean your waffle iron. Heat on the low setting. This loosens the stuck-on sugar. Wipe (carefully) with a damp cloth while the iron is warm.