Preheat oven to 400°F. Line baking sheet with parchment paper and set aside.
In bowl of food processor, pulse together white rice flour, sweet rice flour, tapioca starch, baking powder, salt, and xanthan gum. (Don't have a food processor? Use a medium bowl and whisk ingredients together.) Add shortening and butter.
Cut shortening and butter into dry ingredients by pulsing food processor a few times. Shortening and butter pieces should be about the size of a small peas. (If doing this by hand, cut shortening and butter into the dry ingredients with either a pastry cutter or by rubbing the fats in with your hands.)
Add milk and cheese and pulse until dough forms. (Stir to combine if doing this by hand.)
As soon as dough comes together, stop the food processor.
Drop dough, about ¼ cup each, onto prepared baking sheet. Bake for 18 to 20 minutes or until golden brown.