Make the cookies. In a medium bowl, mix together the flour, salt, and baking powder. Set aside.
In a large bowl using a hand-held mixer, beat together the butter and sugar until light and fluffy, about 2-3 minutes. Add the sourdough discard, egg, lemon zest, lemon juice, and vanilla extract. Mix until combined.
Add the dry ingredients to the wet ingredients and mix until combined, and a smooth dough forms. Wrap the dough in plastic wrap and press it into a disk. Chill in the refrigerator for at least 2 hours (or up to 2 days).
Preheat the oven to 375℉ and line two baking sheets with parchment paper.
Remove the dough from the plastic wrap and divide into two pieces. On a lightly floured surface, use a rolling pin to roll the dough to ¼ inch thickness. Press your cookie cutters into the dough to cut your desired shapes, then transfer the cut cookies to the prepared baking sheet.Gather any dough scraps together, re-roll the dough, and cut out additional shapes until all dough has been used. Repeat with the remaining half of the dough.The dough will be best in the first roll, so get as many cookies out of it as you can! Subsequent rolls will give you slightly thicker cookies (more gluten is activated by gathering and re-rolling the dough).
Bake for 12-14 minutes, until the cookies are firmed and the bottoms are just starting to brown. Transfer the cookies to a cooling rack to cool fully.
Make the frosting. Once the cookies are fully cooled, cream the butter until light and fluffy, 2-3 minutes, then slowly mix in the confectioner's sugar. Add the lemon juice and milk, mixing until fully smooth and incorporated. Add more milk if you feel that the frosting is too thick.
Spread the cookies with a layer of lemon buttercream frosting, add sprinkles (optional), and serve!
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Notes
1 serving = 1 cookieTo make these cookies with active sourdough starter, replace the sourdough discard with active starter (200g). You do not need to change any other ingredients in the recipe.