Preheat oven to 350°F and line a cookie sheet with parchment paper.
Add your dry ingredients to a bowl, stir to mix, and set aside.
Into the bowl of a stand mixer, cream butter and sugar together using the paddle attachment. This can also be done with a hand mixer.
Once butter and sugar are creamed together, add 1 egg yolk at a time and mix until incorporated.
Next, add sourdough discard and vanilla extract. Mix on low speed until combined pausing to scrape down the sides of the bowl.
Add dry ingredients into the mixer 1/3 at a time and mix until the dough just comes together. Do not over-mix.
At this point, you have 2 options. You can portion out the dough into approximately 18 even portions and arrange them evenly on the pan for baking, or you can wrap your dough in plastic wrap to chill before shaping.
For shaping: Chill dough in the refrigerator for as little as 30 minutes or up to 3 days. When you’re ready to shape your cookies, place your dough between 2 pieces of plastic wrap and roll it out using a rolling pin. Use cookie cutters to shape and place unbaked cookies on a prepared baking sheet lined with parchment paper.
When it’s time to bake, place your cookies into a preheated oven and bake for 12-14 minutes just until the bottoms begin to turn a golden brown.
Place cookies on a cooling rack and allow time to cool completely before adding frosting if desired.