Heat oven to 190C/374F/Gas 5.
Line two baking sheets with parchment paper.
Mix the butter and sugar in a bowl until well combined. Add the egg and vanilla and mix well. Add the flour to the mixture and fold in until fully combined and a dough has formed.
Roll the dough out onto a floured surface to a depth of about 5mm. Lay the dough onto the baking sheets and put in the fridge for 10 mins to firm up.
Remove from the fridge and using a 6cm (2 ½ inch) round cutter stamp out 16 base biscuits and 16 top biscuits. With a smaller cutter of around 3cm (1 inch) cut out a hole in the centre of the top biscuits. Place on the baking sheets lined with parchment and leave to cool in the fridge for 10 mins.
Bake the biscuits for 12-15 minutes until golden. Cool on a wire rack.
When cool spread jam on the bottom biscuit and top with another biscuit, sandwiching them together.