Preheat the oven to 190C/170C (fan)/Gas 5. Line a baking sheet with greaseproof paper.
Put the butter, icing sugar, plain flour, cornflour and vanilla extract in a food processor and blend until smooth. You may need to scrape the mixture down a couple of times with a rubber spatula.
Spoon the dough into a piping bag fitted with a large star nozzle. Pipe 16-18 x 6cm/2½in rosettes of the dough, spacing well apart.
Bake in the centre of the oven for 13-15 minutes or until pale golden-brown and firm. Cool on the baking tray for five minutes then transfer to a cooling rack. Repeat with the remaining dough to make 32-36 biscuits.
For the filling, put the butter in a bowl and sift the icing sugar on top. Add the vanilla extract and beat with a wooden spoon or an electric whisk until very light and smooth. Spoon into a clean piping bag fitted with a large star nozzle. Put the jam in a bowl and stir until smooth.
Spoon a little jam onto the flat side of 16 of the biscuits and place jam-side up on the cooling rack. Pipe the buttercream icing onto the remaining biscuits and sandwich with the jam. Put on a serving plate and dust with sifted icing sugar. Serve.