Mix flour, cocoa powder, salt, and baking soda together in a large bowl. Whisk white sugar, brown sugar, butter, shortening, eggs, and vanilla extract together in a separate bowl until smooth. Stir sugar mixture into flour mixture until just combined. Fold in chocolate chips and walnuts.
Spoon batter, 1 to 2 tablespoons per cookie, onto a baking sheet.
Bake in the preheated oven until cookies are browned, 10 to 15 minutes. Cool cookies for 5 minutes on the baking sheet before serving.