Sift together the flours, salt, baking powder, baking soda, and corn starch in a medium-sized mixing bowl.

Cut the chilled butter into 1 inch pieces. Put the white and brown sugars in a stand mixer bowl or large mixing bowl and mix until well combined and no lumps remain. Add cold cubed butter and continue to mix at medium speed. Add eggs, one at a time; continue mixing until well combined.

Add flour mixture to sugar mixture in increments until just incorporated. Stir in chocolate chips and walnuts by hand.

Refridgerate cookie dough overnight.

Preheat oven to 375F.

Using a large spoon or ice cream scoop, place dough onto baking sheets lined with parchment paper. For trays with 6 dough balls, bake about 14-15 minutes, 12 minutes for trays with less dough balls. As is the Levain style, the cookies should be removed from the oven when they look slightly underdone,