Combine white rice flour, teff flour, cornstarch, sweet rice flour, baking soda, xanthan gum, and salt in a bowl.
Beat butter, white sugar, brown sugar, and vanilla extract together in a bowl until smooth and creamy. Add eggs, 1 at a time, beating well after each addition. Slowly beat flour mixture into creamed butter mixture until dough is just mixed; fold in chocolate chips and walnuts. Drop dough by round spoonful onto the baking sheet.
Bake in the preheated oven until cookies are golden brown, 9 to 11 minutes. Let stand for 2 to 3 minutes on the baking sheet before transferring to a wire rack to cool completely.