In a large mixing bowl, cream together the butter and sugar until light and fluffy (2-3 minutes). This can be done with a stand mixer using the paddle attachment, an electric hand mixer, or by hand (you’ll need to use those muscles!).
Add the egg, vanilla, and sourdough starter and mix until smooth and well combined.
Combine the dry ingredients in a bowl: flour, baking powder, baking soda, and salt.
Add the dry ingredients to the wet ingredients, and stir by hand just until combined (you do not want to overwork the dough).
Bring the dough together into a solid mass and shape it into a log or rectangle. Wrap it tightly with plastic wrap or parchment paper (using several layers) and transfer it to the refrigerator.
Chill the dough for at least 30 minutes, but longer is better. Our recommended cold fermentation period is 12 hours to 2 days (see notes** for a breakdown of how short or how long you can ferment the dough).
When you’re ready to bake, preheat the oven to 350°F (175 °C) and line a cookie sheet with parchment paper. Set aside.
Working in batches (leaving the dough in the refrigerator between batches to keep it chilled), roll the dough on a lightly floured surface. It should be about ¼” thick (0.6cm). Using a cookie cutter, cut the dough into shapes or rounds (we used a 3” (7.6cm) round cookie cutter, but various shapes and sizes can be used. Note: Keep an eye on the edges, especially for smaller cookies.
Place the cut-out cookies on the prepared baking sheet. Bake for 9-11 minutes, or until the edges are set, but not browned.
Allow the cookies to cool on the baking sheet for 5 minutes, then transfer them to a wire rack and cool completely before icing.
Repeat with the remaining dough, working in batches until all of the cookies are baked.
Once the cookies are cooled, add your favorite glaze, frosting, sprinkles, etc.