Preheat the oven to 350°F.
Make the biscuit dough: In a mixing bowl, cream together 1/3 cup superfine sugar and 1 stick (1/2 cup) unsalted butter until light and fluffy. Add the listed "a few drops of vanilla extract." If you are using corn starch instead of custard powder for the biscuits, also add the additional 1 tsp vanilla extract listed with that substitution. Sift or whisk together 1 cup all-purpose flour and 8 tablespoons custard powder (or 8 tablespoons corn starch if using the substitution), then fold the dry mixture into the creamed butter and sugar until a workable dough forms. If the dough is very soft or sticky, chill briefly until firm enough to roll.
Roll and cut: Lightly flour your work surface, roll the dough to a thickness of about 1/4 inch, and cut into shapes. Ensure you cut an even number of each shape so you can make pairs.
Bake: Place the cut biscuits on a baking tray lined with parchment paper, leaving a little space between them. Bake at 350°F for about 10 minutes, until lightly golden. Remove from the oven and leave on the tray for a couple of minutes, then transfer to a wire rack to cool completely.
Make the filling: In a bowl, beat 2/3 stick (1/3 cup) unsalted butter (room temperature) with a few drops of vanilla extract until creamy. If you are using corn starch instead of custard powder for the filling, add the additional 1/2 teaspoon vanilla extract listed with that substitution. Gradually add 1 cup powdered sugar and 2 tablespoons custard powder (or 2 tablespoons corn starch if using the substitution), beating until you have a smooth, spreadable buttercream consistency.
Assemble the custard creams: When the biscuits are completely cool, place a heaped teaspoon of the filling on the flat side of one biscuit and sandwich with a matching biscuit. Press gently so the filling spreads to the edges. Repeat with the remaining biscuits.