Preheat the oven to 325°F (163°C). Line a baking sheet with parchment paper.
In a medium bowl, whisk together the gluten-free all-purpose flour, almond flour, xanthan gum, and salt until well combined.
In a large bowl, using an electric mixer, beat the softened butter and granulated sugar on medium speed until light and fluffy, about 2 to 3 minutes.
Add the vanilla extract, freshly grated orange zest, and fresh orange juice to the butter mixture and beat until combined.
Gradually add the dry flour mixture to the wet ingredients, mixing on low speed until the dough comes together and no dry flour remains.
Turn the dough out onto a lightly floured surface and gently knead it just until smooth. Do not overwork.
Roll the dough out to about 1/4 inch (6 mm) thickness.
Using a sharp knife or a pizza cutter, slice the dough into sticks approximately 1/2 inch wide and 3 inches long.
Transfer the cookie sticks to the prepared baking sheet, spacing them about 1 inch apart.
Bake in the preheated oven for 18 to 20 minutes, or until the edges are lightly golden.
Remove from the oven and allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.