Heat oven to 180C and line 2 baking sheets with baking parchment.
Put the butter and icing sugar in a large bowl/stand mixer and beat until pale and fluffy. Add the vanilla.
Sift in the flour, cornflour, baking powder and milk. Fold into the butter/ sugar mixture until combined (the dough should have a thick, stiff consistency but not so stiff you cannot pipe it).
Spoon the dough into a piping bag fitted with a large star-shaped nozzle.
Pipe swirly circles 5cm diameter onto 2 baking sheets. Make sure there are spaces between each swirl as they will expand when baking.
Bake for 10-12 mins, turning the trays around halfway through the cooking time so the biscuits are evenly baked, until pale gold. Leave to cool on the baking sheets for a few mins, then transfer to wire racks.
While the biscuits cool, make the filling. Put the softened butter in a large mixing bowl and add the icing sugar and vanilla. Beat until fluffy and smooth. Transfer the buttercream to a piping bag and snip off the end.
Arrange the biscuits into pairs, turning them over so the flat side is facing up. Spread half of them with jam. I used home-made plum jam that I had left over in a jar.
Pipe the buttercream on the other half.Pair up the biscuits, putting them together until you have a jam half and a buttercream half sandwiched together. Serve with a lovely cup of tea or coffee.