Whisk the white rice flour, tapioca starch, sweet rice flour, salt, and xanthan gum in a large bowl. Cut in the cold butter with a pastry cutter until pea-sized pieces remain.

Drizzle the cold egg and 2 tbsp ice water over the flour. Stir with a fork until the dough holds together when pinched, adding the remaining 1 tbsp water if it's still dry.

Gather the dough into a disk, wrap tightly, and refrigerate for at least 1 hour.

Roll the chilled dough between two sheets of parchment to a 12-inch circle, about 1/8 inch thick.

Preheat the oven to 425°F (220°C). Transfer the dough to a 9-inch pie plate, fold under and crimp the edges, and dock the bottom with a fork. Freeze the pan for 15 minutes. Line with parchment, fill with pie weights, and bake 15 minutes. Remove the weights and parchment, reduce the oven to 375°F (190°C), and bake until deep golden, 15 to 20 minutes. Cool completely before filling.