Use your sourdough discard to make fun cut out sugar cookies! They're soft, thick, not overly sweet, with just a hint of sour flavor from the discard. I'm including my favorite cookie frosting recipe here, too. It's soft and easy to spread (or pipe!), but will still harden enough that you can stack your cookies.
In the bowl of a stand mixer fitted with the paddle attachment, cream together the butter and sugar until light and fluffy. Add the discard, egg, and vanilla and mix until well combined. Don't worry if it looks lumpy at this point! Add the flour, baking powder, and salt and mix until there is no dry flour, scraping down the sides of the bowl as needed. Divide the dough in half, shape into discs, wrap tightly in plastic wrap, and chill for at least 2 hours, up to 24.Preheat oven to 375 degrees. Roll the dough out on a lightly floured piece of parchment paper to ¼-inch thick. Use cookie cutter to cut into your desired shape. Arrange on a baking sheet lined with parchment paper and bake for 5-7 minutes, until baked through and puffed up. DO NOT overbake these! Keep in mind they should not brown.Let cookies cool on the baking sheet for a couple of minutes, then transfer to a baking rack to cool completely. Continue cutting and baking cookies until all the dough is used up. You can smoosh together the scraps and re-roll as many times as needed - be careful not to add too much flour or it will dry out the dough on subsequent re-rolls. If your dough becomes too warm to work with easily, you can wrap it and pop it in the fridge again.Once cookies are cooled completely, you can frost and decorate!
For the Frosting
Add all ingredients (starting with 2 tablespoons of milk) to the bowl of a stand mixer fitted with the whisk attachment. Mix on low speed until no dry bits of sugar remain, scraping down the sides of the bowl as needed. Then, whip on medium-high speed for 2 minutes, until frosting is light and fluffy. If it looks too thick for your liking, add more milk a tablespoon at a time.
Notes
Butter - You can alternatively use ⅓ cup butter and ⅓ cup shortening. I like the flavor of the all-butter cookie better, but the butter+shortening combo makes for cleaner cut cookies.