Preheat oven to 350 F (unless long fermenting.)
In a stand mixer with paddle attachment, cream butter and granulated sugar together for a few minutes until light and fluffy.
Add the eggs in one at a time and mix until well incorporated.
Add vanilla and sourdough discard and mix until just combined. Scrape down the sides a few times.
In a separate bowl, combine the flour, baking soda and salt.
Add the dry ingredients to the wet ingredients about ⅓ at a time, and mix until just incorporated.
Divide the dough into two discs, and wrap with plastic wrap. Place the dough in the refrigerator for at least an hour or for 3 days for long fermentation.
On a lightly floured surface, roll out to ¼” inch thickness between two pieces of parchment paper.
Use cookie cutters to cut out shapes.
Bake for 8-10 minutes or until the edges start to golden.
Allow to cool completely before icing.
In a stand mixer or large bowl add the ingredients. Using a whisk attachment (or a hand held mixer) whip together until peaks form.
If the icing is too thick, add 1 teaspoon of water at a time until the right consistency is reached. If it is too thin, add powdered sugar a tablespoon or two at a time until the desired consistency is reached.
Add to a a piping bag with a tip (or just a ziplock bag with a small corner cut) and decorate the cookies.
