Preheat oven to 350 degrees F (175 degrees C). Generously grease 2 baking sheets.
Beat butter, brown sugar, egg, peanut butter, and vanilla extract together in a bowl until smooth. Mix chickpea flour, cornstarch, baking powder, and salt in a separate bowl; add to butter mixture and mix thoroughly into a cookie dough. Fold chocolate, oats, and nuts into the dough.
Chill dough in refrigerator for at least 15 minutes.
Roll cookie dough into heaping tablespoon-sized balls and arrange on the prepared baking sheets.
Bake in preheated oven until golden brown, 10 to 13 minutes. Let cookies cool on baking rack for 2 to 3 minutes before removing to a wire rack to cool completely.