Cream the butter, both sugars, and salt in a large bowl with a stand or electric handheld mixer for about 5 minutes, until light and fluffy, scraping down the sides of the bowl as needed.
Add the eggs, one at a time, followed by the vanilla.
In a small bowl, whisk together the flour, baking powder, and baking soda, and then swiftly mix into the butter mixture until combined.
Add in the chocolate chips and walnuts until evenly combined.
Scoop the dough into 8 equal portions (roughly 5 ½oz/160g) and place in a single layer in an airtight container. Refrigerate until firm, at least 2 hours or up to 4 days (The unbaked dough can be frozen for up to 2 months. Defrost at room temperature for an hour before baking.)
When ready to bake, preheat the oven to 350°F (180°C) and line 2 baking sheets with parchment paper.
Place 4 balls of dough evenly spaced on the baking sheet without flattening. This big ball of dough will yield you that thick iconic Levain bakery cookie.
Bake on a center rack for 20-22 minutes, until cookies are lightly golden. NOTE: In my oven, I get the best results when I bake one tray at a time.
Let cool for at least 20 minutes before eating. These cookies are best eaten the day they are baked. Store any leftovers in an airtight container at room temperature for up to 1 day.