Preheat oven to 350℉.
Whisk together the flour, cocoa powder, salt, and baking powder in a medium mixing bowl. Set aside.
In the bowl of a stand mixer (or use a hand mixer), cream together the sugar and butter with the paddle attachment on medium speed.
Add the eggs and continue to beat until the mixture is light and fluffy.
Add the sourdough discard and vanilla and continue to stir on medium speed until just combined.
Slowly add the dry ingredients over low speed until almost fully mixed.
Remove the bowl and use a rubber spatula or wooden spoon to stir in the chocolate chips until just combined.
Turn out the dough onto a lightly floured surface. Cut the dough into roughly two equal sized pieces.
Use generously floured hands to shape each dough half into a rectangle that measures approximately 12 inches long, 2 inches wide, and 1 inch thick. If the dough becomes too sticky, add more flour to your hands and work surface as needed.
Place each dough log on a large baking sheet lined with parchment paper, spacing them 2 inches apart.
Bake in preheated oven for 25-30 minutes or until the dough feels firm to the touch and the top has started to crack.
Remove from the oven and allow to cool for 30 minutes.
Transfer each large biscotti to a cutting board and use a large serrated knife or sharp kitchen knife to cut the biscotti into 1 inch wide pieces.
Arrange the individual biscottis to the baking sheet, cut side up.
Bake for another 30 minutes, flipping the biscotti halfway through.
Allow to cool completely before serving.