Preheat oven to 410 degrees.
In a large mixing bowl, cream together cold cubed butter and brown sugar for 4 minutes or until creamy.
Add eggs, one at a time, mixing well after each one.
Stir in flours, cornstarch, baking soda, and salt. Mix until just combined to avoid overmixing.
Stir in chocolate chips and walnuts.
Separate dough into large balls and place on lightly colored cookie sheet.
Bake for 9-12 minutes or until golden brown on the top. Let them rest for at least 10 minutes to set.