Preheat the oven to 180°C (350°F) or 160°C (320°F) fan and line 2 baking sheets with parchment paper.
Beat butter and sugar in a large bowl until creamy, about 1 minute on medium speed.
Add the egg and vanilla extract, beating until fully combined.
Gradually add flour, baking powder, and salt. Mix slowly at first, then beat until fully incorporated; the dough will be slightly clumpy.
Dust your work surface with flour. Scrape dough onto the surface, pat into two discs, and roll out to 0.3 cm (1/8") for thin, crisp cookies or 0.6 cm (1/4") for thicker, softer cookies. Sprinkle flour underneath and over the dough to prevent sticking.
Use cookie cutters to press out shapes. Transfer shapes to prepared baking sheets using a knife or spatula. Keep any unused dough refrigerated.
Bake for 10 minutes, swapping trays halfway through, until the surface is pale golden and edges just start to turn light golden.
Allow cookies to cool completely on the baking sheets. They will finish cooking as they cool.
Decorate as desired: with icing, melted chocolate, silver balls, a dusting of icing sugar, or serve plain.