In the bowl of a stand mixer, add the butter and sugar. Beat on medium speed for 2 minutes until the mixture is light and fluffy.
Add the egg, vanilla extract, and sourdough discard. Mix again for 1 minute.
Carefully add the flour and salt to the stand mixer. Mix for 1 minute until the dough comes together into a ball.
Wrap the dough ball in plastic wrap and make the dough ball into a disc. Place in the refrigerator for at least an hour, or up to overnight.
When you are ready to bake the cookies, preheat the oven to 350 degrees.
Lightly flour your countertop and place the dough on the flour lined counter. Flour a rolling pin and roll the dough out so the thickness of the dough is about ¼ inch thick.
With your favorite cookie cutters, cut the dough, and place the cut outs onto a parchment lined baking sheet. If you are adding sprinkles to the cookies, now is the time to add them. Bake for 8-12 minutes depending on the thickness of your cookies.
When they are baked, allow them to cool on a wire cooling rack and then decorate with royal icing.