Line a large tray or two with baking paper.
In a large bowl, beat the butter and sugar together until smooth. Then mix in the vanilla extract and the egg.
Add in the flour, baking powder and salt. Mix well and when it starts to stick, use your hands to press everything together into a ball of dough.
Pop the ball of dough in the fridge for 30 minutes to chill.
While the dough is chilling, preheat your oven to 180°C/350℉ (or 160°C/320℉ for fan or convection ovens).
Gently knead the cookie dough in your hands to get rid of any cracks then roll the dough out on a lightly floured surface until it's around ¼-inch thick.
Use a 3-inch round cookie cutter to cut out your cookies, re-rerolling leftover pieces of dough until it's all used up.
Bake for 10-11 minutes, until they are firm around the edges and slightly soft in the middle. They will firm up more as they cool.
Leave them on the tray to cool completely.