Line a cookie sheet with parchment paper.
Whisk all-purpose flour, cake flour, baking powder, baking soda, and salt in a medium bowl. Set aside
Using a hand mixer or a stand mixer (fitted with the paddle attachment), cream the cold butter on low speed until the cubes lose their shape, about 45 seconds to one minute. Add both sugars and cream about 1 minute more.
Add eggs and vanilla and mix until smooth, then mix in the dry ingredients until thick.
Add chocolate chips and walnuts and stir to combine.
For authentic sized cookies, shape large balls of cough, about 6 ounces (172g) each (approximately ¾ cup). Set on the prepared cookie sheet. Chill for at least 90 minutes, up to overnight. (If chilling longer than 90 minutes, be sure to cover the pan with plastic wrap).
Preheat oven to 375°F. Place an empty cookie sheet upside down on the middle rack.
Remove cold dough balls and spread to a second cookie sheet (4 cookie dough balls per large cookie sheet).
Bake one sheet at a time, on top of the upside down sheet on the middle rack. Bake approximately 20-26 minutes. Check after about 15 minutes to see if the pan needs to be rotated, depending on how your oven bakes. When done, the cookies will loose their glossy sheen, edges and spots on top will be a dark golden, and the insides will still be slightly doughy.
Cool cookies at least 10 minutes on pan before removing and enjoying.
Store cookies in an airtight container at room temperature for up to 4 days. Freeze baked and cooled cookies for up to 3 months. Cookie dough can also be frozen. To bake from frozen, add 2-3 min to the cook time.