Preheat your oven to 180°C / 350°F (or 160°C fan-assisted). Prepare two baking trays by lining them with parchment paper.
In a large mixing bowl, cream the softened butter and sugar together until the mixture turns smooth and fluffy. This should take about one minute at medium speed.
Crack in the egg and pour in the vanilla extract, beating the mixture again until the ingredients are fully incorporated.
Sift the flour, baking powder, and salt into the bowl. Start mixing on a low speed to prevent a flour cloud, then increase to a medium speed until the dough comes together. It will look crumbly but should hold its shape when pressed.
Lightly dust your work surface with flour. Transfer the dough from the bowl and press it together. Divide into two portions and form each into a disc shape.
Roll out each disc on the floured surface to your preferred thickness: 0.3 cm / 1/8 inch for crisp cookies or 0.6 cm / 1/4 inch for softer ones. Sprinkle a bit of flour over and under the dough as needed to prevent sticking.
Use cookie cutters to create festive shapes, carefully transferring them onto the prepared baking trays with a knife or spatula. Store any remaining dough in the fridge while batches bake.
Bake in the preheated oven for about 10 minutes, rotating the trays halfway through for even baking. The cookies are ready when their surfaces are pale golden and the edges show a light golden hue.
Allow the cookies to cool completely on the trays. They will continue to firm up as they cool.