Heat the oven to 190°C/170°C fan/ gas 5. Line 2 large baking sheets with baking paper.
Using an electric mixer, beat the butter, icing sugar, plain flour, cornflour, lemon zest, vanilla extract and milk in a large mixing bowl until smooth and creamy.
Spoon into a piping bag fitted with a star nozzle, then pipe 24 circular swirls, roughly 5cm in diameter, onto the lined sheets, leaving the same size gap between each biscuit. Chill for 15 minutes or up to 2 hours.
Bake in the oven for 16-20 minutes until pale golden. Remove from the oven and leave on the sheets for 5 minutes before carefully transferring the whirls to a cooling rack to cool.
Meanwhile, make the filling. Using an electric mixer, beat the butter, icing sugar and lemon juice in a large mixing bowl. Transfer to a piping bag.
When the biscuits have cooled, carefully pipe a little icing on the flat side of 12 of the biscuits. Spoon a little jam on top, then top with another biscuit. Keep refrigerated until serving.