Line a sheet pan with parchment paper and set aside.
In a medium-sized mixing bowl, combine the gluten-free flour, sifted cocoa powder, baking powder and xanthan gum. Set aside.
In a large mixing bowl, combine the melted butter with the granulated sugar, vanilla and salt. Then add the eggs and stir until they're fully incorporated and the mixture is smooth.
Add the dry ingredients and mix until you no longer see any dry spots.
Remove 1 tablespoon of the crushed candy canes and set aside for garnish. Fold the rest of them into the dough, with the semisweet chocolate chips and white chocolate chips.
Shape the cookie dough into balls, about 1 1/2 tablespoons each. Roll them between your hands to make them smooth, placing them on the parchment-lined sheet pan as you go. Cover tightly with plastic wrap and refrigerate until firm, at least 1 hour, and up to a couple of days.
About 15 minutes before you're ready to bake, preheat the oven to 350°F, adjust a rack towards the center of the oven and line another sheet pan with parchment paper.
Add the powdered sugar to a shallow bowl. Gently roll each ball of refrigerated dough through it -- placing them on the parchment-lined sheet pan as you go, with a couple inches between them. Sprinkle each one with a pinch of the tablespoon of crushed candy canes that were set aside.
Bake in the preheated 350°F oven just until they no longer look doughy, have flattened out by about 50% and are "crinkled," about 8 minutes. Let them cool on the baking sheet for at least 15 minutes.
Repeat until all of the cookies are baked.