Beat the butter and sugar in a stand mixer on medium speed for 2-3 minutes, until light and creamy. Incorporate the egg and vanilla and thoroughly mix.
Sift in the flour and custard powder and mix by hand to a crumbly dough. Bring the dough together with your hands and knead it gently on a lightly floured work surface until smooth. Do not overwork the biscuit dough.
Split into discs, wrap and chill for 1 hour.
Roll dough to 3mm thick. Lightly flour the custard cream biscuit cutter and stamp, then cut out and stamp the biscuits, flouring the cutter and stamp each time. Chill for 30 minutes.
Preheat oven to 170°C/150°C fan. Bake the biscuits for 12-14 minutes, until the edges start to turn a golden colour. Leave them to cool on the baking sheets for 5 minutes, then transfer them to a wire rack to cool completely.
Tip the sugar into a small pan, add 2 tablespoons of water and bring it to the boil. Boil the mixture until the temperature on the sugar thermometer reaches 115°C.
Put the egg yolks in the bowl of stand mixer fitted with a whisk and whisk on low speed. Slowly and carefully pour the hot sugar syrup over the egg yolks, then increase the speed to high and whisk until the mixture is thick and leaves a ribbon trail when you lift the whisk. Sift the custard powder over the surface of the mixture and whisk again until the mixture is cool to the touch.
Whisk in butter gradually, then transfer to a piping bag and chill.
Pipe crème au beurre on half the biscuits, then sandwich with remaining biscuits.
Chill until the filling is firm. Store up to 3 days in an airtight box.
Notes
If custard powder is not available, you can substitute it with an equal amount of cornflour (cornstarch) mixed with vanilla essence for the biscuit dough. The custard powder primarily acts as a thickening agent and adds a vanilla flavour. It also adds some colour, so you might want to add turmeric, saffron or food colouring, too.