Melt the unsalted butter in a medium-sized saucepan and let it cool off to the side.
Roughly chop the dark chocolate into smaller pieces.
In a medium-sized bowl, mix together the all-purpose flour, cake flour, cornstarch, kosher salt, and baking soda.
Use a stand mixer with the whisk attachment. Put the light brown sugar and granulated sugar in the mixer and whisk at medium speed. Slowly pour in the melted butter.
Once combined, add the eggs one at a time, followed by the egg yolks.
Switch to the paddle attachment and gradually add the flour mixture until the batter is smooth.
Stir in the chopped walnuts and dark chocolate until evenly combined.
Place the dough in a bowl, cover it, and refrigerate for at least 45 minutes.
Preheat the oven to 425°F (218°C).
Take out the chilled dough and weigh each portion to 6 ounces. Place the portions on a baking sheet lined with parchment paper.
Bake the cookies in the preheated oven for 11-13 minutes.
Once baked, transfer the cookies to a wire rack to cool before serving.
Enjoy your delicious homemade Joshua Weissman-style chocolate walnut cookies!