Preheat oven to 375 degrees F (190 degrees C). Line a baking sheet with parchment paper.

Beat the butter, brown sugar, and white sugar together with an electric mixer in a large bowl until smooth. Beat the eggs, one at a time, into the butter mixture until completely blended; add vanilla extract.

Whisk cornstarch, sorghum flour, sweet rice flour, brown rice flour, almond meal, cinnamon, baking soda, and salt together in a bowl. Stir flour mixture into butter mixture; add oats and mix to form a soft dough. Roll dough into walnut-sized balls and place 2 inches apart onto prepared baking sheet.

Bake in the preheated oven until cookies are golden and set, about 10 minutes. Cool cookies on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.