Preheat the oven to 180°C, fan 160°C, gas 4.
In a medium bowl, beat together the butter and sugar until light and fluffy. Beat in the egg yolk and the vanilla extract. Stir in the flour and then, using your hands, lightly knead to form a ball.
On a lightly floured work surface, roll out the dough to a 5mm thickness. Using an 8cm star-shaped cookie cutter, stamp out 24 stars, then stamp out little stars from the middle of 12 of the biscuits using a 2-3cm star cutter. Place the biscuits on baking parchment-lined baking trays and put in the freezer for 10 minutes.
Spread a thin layer of jam on to the whole large stars, placing the stars with cut-out middles on top. Bake for 10 minutes until lightly golden. Allow to cool on a wire rack, then dust with icing sugar to serve.