Whisk together white rice flour, corn powder, corn flour, baking powder, baking soda, and salt in a medium bowl. Set aside.

Combine butter and sugar in the bowl of a stand mixer fitted with the paddle. Beat at medium-high speed for 2 minutes. Turn off mixer and scrape down the bottom and side of the bowl and the paddle with a rubber spatula. Add egg mix at medium-high speed until very light and airy, about 7 minutes. Scrape down the bottom and side of the bowl and the paddle attachment once more.

Add the dry ingredients and turn mixer to medium-low speed. Mix until dough comes together, about 1 minute. Scoop the dough using a #40 cookie scoop (about 1 1/2 tablespoons each) onto a parchment-lined rimmed baking sheet. Using the bottom of a drinking glass dusted with white rice flour, press down lightly on each cookie to flatten. Wrap the baking sheet tightly in plastic and refrigerate for at least 2 hours and up to 3 days.

Center oven rack in middle position and preheat oven to 350°F. Line two rimmed baking sheets with parchment paper. Place 6 dough balls about 4 inches apart on one of the parchment-lined baking pans.

Bake until cookies are golden brown, about 15 minutes. Allow cookies to cool on for 5 minutes. Using a metal spatula, transfer cookies to wire rack to cool completely. Store cookies in an airtight container for up to 4 days. Repeat with remaining batter, alternating baking sheets between each batch so that you are always baking on a cool sheet. Store cookies in airtight container on the counter for up to four days.