Line a couple of baking sheets with baking parchment.
Cream the butter, sugar, vanilla and milk together in a large bowl until smooth. Don't beat the mixture for too long, you don't want to incorporate too much air.
Add the custard powder and stir until combined.
Add the flour and mix to form a soft, smooth dough. If the dough feels too soft to roll out, wrap it and chill it in the fridge for 30-60 minutes until it has firmed up a bit..
Roll the dough out on a lightly floured surface to about 4mm thick and use your choice of cutter to cut out as many cookies as possible. Bring together the scraps and re-roll to cut out more cookies.
Place the cookies slightly spaced apart on the lined baking sheets and place in the freezer for 15 minutes. Meanwhile, preheat the oven to 180℃/160℃ fan/350℉/gas mark 4.
Bake the biscuits for 12-15 minutes until pale golden. Allow to cool on the baking sheets foor a minute or two then carefully transfer to a wire rack and leave to cool completely.
To make the buttercream, whisk the butter until smooth then add the vanilla, custard powder and icing sugar and whisk until smooth and fluffy.
Spread a thin layer of buttercream over the base of half of the biscuits, top each one with another biscuit, gently pressing it onto the buttercream.