Put the butter and sugar in a large bowl and beat with an electric whisk until pale and fluffy. Beat in the eggs, one at a time, followed by the vanilla extract.
Sift in the flour, baking powder and 1/2 tsp salt and combine with a spatula to form a soft dough.
Divide the dough into two balls and flatten each half in a disc. Wrap in clingfilm and chill for 1 hour to firm up.
Preheat the oven to gas 4, 180C, fan 160C and line three large baking sheets with nonstick baking paper. Dust a clean work surface generously with flour, then remove one disc from the fridge and cut it in half (this will make it easier to roll). Roll out one half at a time to around 1/2cm (1/4in) thick. Using a round 7.5cm (3 1/4in) biscuit cutter, stamp out 10 rounds from each half. Transfer the rounds to the baking trays with a palette knife, leaving a small gap between each one.
Using a 6-6.5cm (2 1/2 - 2 3/4 in) star-shaped biscuit cutter, stamp out star shapes in the middle of half the biscuits. Repeat with the remaining chilled dough to make about 40 biscuits - 20 bases and 20 with stars stamped out. You will need an even number of bases and star-shaped rounds for sandwiching the biscuits.
Bake for 8-10 minutes, until lightly golden. Leave to cool on the baking sheets for a few minutes, then transfer to a wire rack to cool completely.
To make the buttercream filling, combine the butter, icing sugar and vanilla in a large bowl. Beat with an electric whisk until light and soft. It may feel a little stiff at first, but continue beating and the mixture will eventually come together.
To assemble the biscuits, spread a teaspoon of buttercream over the base of each whole biscuit. Top the layer of buttercream with a layer of jam, putting most of the jam in the centre, and just a thin covering at the edges. Gently press the stamped-out star biscuits on top and dust with a little icing sugar.