Preheat your oven to 180°C (350°F).

In a mixing bowl, cream together the unsalted butter and superfine sugar until light and fluffy, about 2-3 minutes.

Add the egg, egg yolk, and vanilla extract to the butter-sugar mixture and blend until creamy.

Incorporate the cake flour and salt, folding until just combined.

Scoop tablespoon-sized portions of dough onto a lined baking sheet with space between each to allow for spreading.

Bake for about 10-12 minutes or until the edges are golden. The centers may look slightly underbaked but will firm up as they cool.

Allow cookies to cool on the baking sheet for about 5 minutes before transferring to a wire rack.

In a separate bowl, cream the room temperature butter with sifted powdered sugar.

Mix in the milk and vanilla extract until smooth and glossy.

Once cookies are completely cooled, spread or pipe the buttercream on top.

Let the buttercream set before serving.