Preheat the oven to 180 °C (160 °C fan). Line baking sheets with parchment paper.
In a large bowl, beat the softened butter and sugar until smooth and creamy.
Add the egg and vanilla, and mix until fully combined.
Stir in the flour, baking powder and salt. Mix just until the dough forms — it may look a little crumbly.
Lightly flour your work surface. Divide dough if needed, and roll it out to your desired thickness: about 0.3 cm (for crispier cookies) or 0.6 cm (for softer, thicker cookies).
Use cookie cutters to cut out shapes, and transfer them carefully to the prepared baking sheets. Gather and re-roll scraps of dough as needed.
Bake in preheated oven for about 10 minutes — cookies should be pale golden, with edges just beginning to turn light golden.
Let cookies cool completely on the trays, as they continue to set while cooling.
If you like, decorate with icing, melted chocolate, sprinkles or a dusting of sugar once cool.