Mix the dry ingredients: In a medium bowl, whisk together the almond flour, coconut flour, tapioca starch, and baking powder. Set aside.
Cream the wet ingredients: In a separate large bowl, beat the shortening, egg, and sugar with a handheld or stand mixer until creamy and fully combined.
Combine wet and dry: Gradually add the dry ingredients to the wet mixture, mixing until a dough forms. If the dough feels too sticky, add 1-2 tbsp additional tapioca starch until it’s workable.
Chill the dough: Wrap the dough in plastic wrap and chill in the freezer for 20 minutes (or at least 1 hour in the fridge).
Roll and cut: Preheat the oven to 350°F and line a baking sheet with parchment paper. Roll out the dough to about 1/4 inch thick on a floured surface (use tapioca starch for dusting). Cut into your favorite shapes using cookie cutters.
Bake: Place cookies on the prepared baking sheet and bake for 8-10 minutes, or until edges are just lightly golden. Keep an eye on smaller shapes to prevent over-baking. Allow cookies to cool completely on a wire rack before icing.