Preheat oven to 350°F. Line the sides and bottom of an 8 x 8-inch baking pan with aluminum foil, leaving an overhang of about 2-inches on each of two opposite edges. Cut a piece of parchment paper to fit the bottom of the pan. Place parchment on top of foil.
In a medium bowl, sift together brown rice flour, potato starch, tapioca flour, and xanthan gum. Whisk in almond flour. Set aside.
In the top of a double boiler, set over simmering water, melt unsweetened chocolate and butter. Stir constantly, until chocolate and butter are fully combined and mixture is smooth. Remove from heat and let cool to room temperature.
In the large bowl of an electric mixer, combine eggs, sugar, salt, and vanilla extract. Set mixer speed to high and beat until mixture thickens and becomes pale in color, about 1 to 2 minutes. Turn off mixer. Using a rubber spatula, fold chocolate mixture into egg mixture. Take care not to deflate the batter. Fold in flour mixture in two portions. Carefully fold in walnuts and chocolate chips.
Pour batter into prepared baking pan. Smooth top. Bake until top is slightly cracked and just firm to touch, about 35 to 40 minutes. Cool uncut cookies in baking pan on a wire rack. Lift uncut cookies out of pan, using foil overhang as an aid, and cut into 16 cookies.
Store cookies in an airtight container, at room temperature, for up to 3 days, or refrigerate for a longer shelf life.
Baker’s Notes: Pecans or toasted hazelnuts can be substituted for walnuts.