1. Preheat oven to 350°.
2. Weigh or lightly spoon potato starch, cornstarch, and flours into dry measuring cups; level with a knife. Combine potato starch, cornstarch, flours, xanthan gum, and salt in a medium bowl, stirring with a whisk.
3. Place 1/2 cup powdered sugar, butter, and vanilla in a large bowl; beat with a mixer at medium speed until well blended. Add canola oil, milk, and egg yolks, beating until blended. Gradually add flour mixture, beating until blended. Stir in pecans.
4. Shape dough into 38 (1-inch) balls, and place 2 inches apart on baking sheets lined with parchment paper. Flatten tops of cookies slightly with fingers. Bake at 350° for 10 to 12 minutes or until bottoms of cookies are lightly browned.
5. Immediately roll warm cookies in 1/3 cup powdered sugar; cool completely on a wire rack, reserving powdered sugar. Reroll cooled cookies in remaining powdered sugar.