Sift cornstarch, icing sugar, sweet rice flour, tapioca, sorghum, and white rice flours together in a large bowl. Blend in butter until a soft, smooth dough forms.

Shape dough into 1-inch-thick logs. Wrap in plastic and refrigerate until firm, 30 to 60 minutes.

Preheat the oven to 300 degrees F (150 degrees C).

Slice cold dough into 1/8-inch rounds. Place rounds 1 1/2 inches apart on a cookie sheet.

Bake in the preheated oven until edges are firm and tops are still pale, 15 to 20 minutes. Transfer to a rack to cool.