Line a baking sheet with parchment paper; set aside.
In a medium bowl, whisk together the flour, baking powder, baking soda and salt; set aside.
Using an electric mixer, beat the butter on medium speed until it comes together in one cohesive mass, about 1 minute. Add both sugars and continue to beat for another 1 to 2 minutes, until all of the sugar has been incorporated into the butter. Gradually add the eggs and vanilla and continue beating on medium speed until combined, scraping the sides of bowl once (the batter will appear lumpy). Reduce the speed to medium-low and gradually add the flour mixture until just a little bit of flour still remains. Stir in the chocolate chips and walnuts with a rubber spatula.
Divide the dough into 12 even pieces, roughly shaping them into balls (it should not be smooth). Place them,evenly spaced, on the prepared baking sheet. Refrigerate for 30 minutes.
Preheat oven to 375 degrees F.
Bake for 18 to 24 minutes, or until light golden brown on top. Let cool for 5 minutes on the cookie sheet, then remove to a wire rack to finish cooling. Leftovers can be stored in an airtight container at room temperature for up to 4 days.
While dark chocolate chips mimic the original recipe, you could also use semisweet chocolate chips.
You can omit the walnuts for allergy purposes or personal preference.
To get cookies all the same size, I recommend using a scale for weighing out the dough.