In the bowl of a stand mixer fitted with the paddle attachment, or using an electric hand mixer, cream together the butter and sugars until combined and fluffy, about 5 minutes. Add the egg and vanilla and mix until well incorporated.
Add the flours, cornstarch, baking soda, and salt, and use a rubber spatula to gently fold until just combined. Fold in the chocolate chips and walnuts.
Separate the dough into four large, 6 oz hockey-puck-shaped cookies about an inch thick, then place onto a parchment paper-lined baking sheet. Cover with plastic wrap and place in the fridge for 30 minutes.
Preheat the oven to 400°F (200°C).
Bake for 15-16 minutes or until light golden brown on the top. Let them rest for at least 10 minutes to set.
*Using cake flour makes a more tender cookie but you can substitute all-purpose flour if that's all you have!