Preheat the oven to 350°F. Line an 8×8-inch baking pan with parchment paper. Do not grease.
In the bowl of a stand mixer fitted with a paddle attachment, or using a hand mixer, add the butter and mix on medium speed for just 10 seconds, until slightly softened without any air incorporated.
Add the powdered sugar and vanilla and mix for 10 seconds, until just incorporated.
Add the gluten-free flour and salt and mix for 15-20 seconds, until just barely combined. If the mixture still has dry streaks, use your hands to knead the dough in the bowl until the flour is fully combined. Do not overmix.
Press the dough into the prepared pan.
Bake for 45-50 minutes, until the edges are lightly golden. Remove from the oven and immediately sprinkle with sanding sugar.
Place the baking pan on a wire rack and cool for 10-15 minutes before slicing. You want the shortbread to be slightly warm when you slice it.
Transfer the shortbread to a cutting board. Slice the warm shortbread into 6 rows, then 3 columns to make rectangles.
Transfer the shortbread to a wire rack to cool completely.