In a large mixing bowl, cream the cold cubed butter, brown sugar, and granulated sugar on medium speed for about 4 minutes until light and fluffy.
Add eggs one at a time, mixing thoroughly after each addition.
Gradually add cake flour, all-purpose flour, cornstarch, baking soda, and salt. Mix until just combined.
Fold in the chocolate chips and roughly chopped walnuts with a spatula until evenly distributed.
Divide the dough into 10 large balls, about 5 ounces each.
Preheat your oven to 410°F (210°C).
Place dough balls on a parchment-lined baking sheet, spacing them out to allow for spreading.
Bake for 9–12 minutes, or until the edges are golden and the centers are just set.
Allow the cookies to cool on the baking sheet for about 5 minutes before transferring them to a wire rack to cool completely.