In the bowl of a stand mixer fitted with a paddle attachment*, cream the butter and sugar until fluffy, 2-3 minutes. Add the sourdough discard, orange zest and vanilla extract, mixing until combined. You may need to scrape down the sides of the bowl.
Add the flour and salt, then mix on low speed until combined. Increase speed to medium and mix until a dough forms.
Turn the dough onto a work surface and divide in half. Shape each piece into a rectangle (or your desired shape), approximately 2 inches wide and 1 inch thick. Wrap the dough in plastic wrap and transfer to the refrigerator to chill for at least one hour.
Preheat the oven to 350℉ (180℃). Line to baking sheets with parchment paper and set aside.
Unwrap the chilled dough and use a sharp knife to cut into ¼-inch thick slices. Transfer the slices to the baking sheet, leaving 2 inches between each cookie (they will expand as they bake).
Bake one sheet at time for 12-14 minutes until the cookies are just becoming golden brown at the bottom edges. They will still be very pale overall. Transfer the cookies to cool on a wire rack for at least 15 minutes.
In a small bowl, mix 2 Tablespoons granulated sugar with ½ teaspoon orange zest. Set aside.
Once the cookies have cooled, melt 3-4 ounces of dark chocolate in a small pot or double boiler over low heat. Dip the ends of each cookie into the chocolate, then return to the wire rack (or a parchment paper-lined baking sheet). While the chocolate is still warm, sprinkle with the sugar and orange zest mixture. Let the cookies cool completely before serving.
Video
Notes
*You can make this recipe without a stand mixer, using a large mixing bowl and hand-held mixer. To make this recipe with active sourdough starter, replace the sourdough discard with active starter (133 grams). You will not need to change any of the other ingredients.