Cream the butter and sugar together until fluffy.
Then, add the lemon zest, vanilla, eggs, sourdough discard, and buttermilk.
Mix in the flour until hydrated.
Preheat the oven to 350ºF (177ºC) and prepare two baking sheets with parchment paper.
Use a cookie scoop to portion out 14 cookies, a few inches apart.
Ice the vanilla or white half of all of the cookies first. Let set for 20 minutes.
Then, mix in cocoa powder to the same icing mixture and ice the remaining cookies.
Black and White Cookies store well for a few days at room temperature, and up to a week in the refrigerator.
You can even freeze the baked cookies for long-term storage!