Begin by preheating your oven to 180°C. Prepare two baking trays by lining them with baking paper.
In a small mixing bowl, use an electric mixer to cream together the softened butter, caster sugar, and vanilla extract until the mixture becomes pale and fluffy. Crack the egg into the bowl and mix until fully incorporated. Sift the flour and baking powder into the butter mixture, then pour in the milk. Gently fold the ingredients together until they are just combined, ensuring not to overmix.
Take small portions of the dough, approximately 2 teaspoons each, and roll them into smooth balls. Arrange the dough balls on the prepared baking trays, leaving enough space between them for spreading during baking. Lightly flour a fork and gently press down on each ball to slightly flatten the biscuits.
Bake in the preheated oven for 12 to 15 minutes, rotating the trays after the first 10 minutes, or until the biscuits turn a light golden color. Once baked, allow the biscuits to rest on the trays for 5 minutes before transferring them to wire racks to cool completely. Finish by dusting the cooled biscuits with icing sugar, and they are ready to be served.