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, and vanilla extract and 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℉ (190℃) 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.
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.
Using a hand-held mixer, cream the butter in a medium-sized bowl on low speed until light and fluffy, about 2-3 minutes. Slowly add in the sifted confectioner's sugar (I like to do this in 3-4 portions, mixing in between each). Add the vanilla extract and milk, mixing until smooth and combined. Add food coloring and mix to reach your desired color.
Spread the cooled cookies with buttercream frosting, then top with Halloween sprinkles and edible candy eyeballs.
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Notes
1 cookie = 1 serving. Nutrition information is calculated without sprinkles. While it's not needed for leavening purposes, you can make these cookies with active sourdough starter. To do so, replace the sourdough discard with active starter (200g). Be prepared that your cookies may rise more than the version made with discard.