Combine cake flour, all-purpose flour, cornstarch, baking powder, and salt in a bowl.
In a large mixing bowl, whisk sugar and melted butter on medium speed. Add egg one at a time.
Stir in the flour mixture. Mix until just combined to avoid overmixing.
Stir in walnuts and chocolate chips. Leave the dough in the fridge for 45 minutes - 1 hour.
Separate the dough into balls using an ice cream scoop on a light-colored cookie sheet, then leave the dough in the fridge. Meanwhile, preheat the oven to 375F.
Bake cookies for 8-10 minutes or until golden brown. Let them rest for at least 10 minutes to set.