Add all purpose flour, baking powder and salt to a mixing bowl and whisk together until well combined. Set this aside.
Add the butter and sugar to a mixing bowl and cream them together using a hand mixer until they are light and creamy (you could also do this in a stand mixer if you prefer).
Add the egg, vanilla extract and sourdough starter to the butter and sugar mixture and beat on medium speed until well combined.
Now, add the wet mixture to the dry ingredient mixture and combine into a soft dough (use low speed on hand mixer or stand mixer or wooden spoon). Don't over mix the dough, it needs to just come together.
Divide the mixture into two balls and place each ball between two sheets of parchment paper.
Use a rolling pin to roll each ball of dough into a "sheet" of dough around half a centimetre thick (¼ inch). Place each sheet of dough onto a flat cookie sheet and place them into the fridge. If you don't have room, just stack the two sheets on top of each other.
Allow the dough to sit in the fridge overnight if you can (up to 48 hours).
When you are ready to bake the sourdough sugar cookies, preheat the oven to 175C (350F).
Take one sheet of dough out at a time and cut the cookies out with a cookie cutter (see notes for how to deal with excess dough). Place the shaped dough onto the cold cookie sheet lined with parchment paper. You want to leave around 5 cm (2 inches) between each cookie.
Place the cookies into the oven for 10 to 12 minutes (watch them closely). You don't want them to brown too much.
Take the cookies out of the oven and allow them to sit on the tray for around 5 minutes before placing them on a wire rack to cool completely.
You can decorate these cookies however you'd like. Royal icing is great if you want to pipe a design on. The white stars and pink circle cookies in these photos have been decorated using fondant icing which I rolled out really thing and cut to the same shape. The cookies with sprinkles were topped with a glaze and then dipped in sprinkles.