In large mixing bowl, cream together cold cubed butter, brown sugar, and sugar for 4 minutes or until creamy.
Add eggs, one at a time, mixing well after each one, then the vanillas.
Stir in flours, cornstarch, baking soda, and salt. Mix until just combined. Fold in chocolate chips and walnuts.
Use a 2.66oz cookie scoop to scoop dough into large balls and place on lightly colored cookie sheet. You should be able to get 15 cookies, and I recommend baking them 5 to a cookie sheet.
Bake for 11 minutes or until golden brown on the top. Let cookies rest for at least 10 minutes before eating.