To make the biscuits, mix together the butter and sugar in a bowl with a wooden spoon until well combined. Add the egg and vanilla, and continue to beat by hand until fully incorporated. You will need to scrape the edges of the bowl down for this part.
Tip the flour into the mixture and fold together until fully combined, then shape into a ball. Roll the dough out onto a floured sheet of baking parchment to a depth of around 5mm. Transfer the sheet to a baking tray and put in the fridge for 10 mins to firm up.
Remove from the fridge and press out your biscuits using a 6cm cutter. You will need 16 base biscuits and 16 top biscuits, with small holes of around 3cm cut out of them.
Recombine your dough off-cuts and reroll them on a floured surface. Try to be fairly quick doing this, as the mixture will warm up and get sticky. If it does, just pop it back in the fridge to firm up again.
Once the shapes are cut out, arrange on 2 baking sheets lined with baking parchment and leave to cool in the fridge for 10 mins.
Heat oven to 190C/170C fan/gas 5. Bake the biscuits for 7 mins, then take them out of the oven and sprinkle the tops with caster sugar. Return all the biscuits to the oven and cook for a further 5 mins. Take out and allow to cool fully on a wire rack. When cool, spread jam on the bottom biscuit and top with another biscuit, with a hole in it, sandwiching them together. Will keep for 2-3 days in an airtight container.