1. Stir the fresh yeast into the buttermilk in a large bowl, or the bowl of the standing mixer (it will be a real chore to knead it by hand). Sprinkle a spoonful of sugar and leave to foam up a little, about 30 minutes.
2. Add the remaining sugar, flour, salt and eggs to the bowl and mix with a dough hook attachment for 10 minutes at high speed until the dough gathers into a ball and, ideally, bounces off the walls of the bowl.
3. Turn the speed down to medium and add the butter by a tablespoon, waiting for each one to be absorbed. Scrape the sides of the bowl if necessary. The dough should be smooth, glossy and very sticky. Place it in a lightly oiled bowl in a warm place for 2 hours, till it doubles in volume; then chill it in the fridge overnight.
4. Turn the dough gently onto a lightly floured surface. Divide it into 4 equal pieces and gather them into balls. Cover them with a tea towel and leave for 15 minutes.
5. Prepare the three fillings: stir together the cocoa, sugar and vegetable oil, then add some of the beaten egg (for brushing) to make a spreadable paste. In another bowl stir cinnamon with sugar, and in the third – the apple preserve with ground almonds.
6. On a lightly floured surface roll out each piece to a disc, about 30cm in diameter so fairly thin. You can stack them, separated with sheets of parchment. Place the first layer on parchment on a large baking sheet. Mark a neat circle using a plate or a large pan. Spread the cocoa filling thinly, leaving a 1cm rim.
7. Transfer the next pastry disc on a rolling pin and lay it over the first. Spread the apple filling, leaving a rim again. Repeat with the next pastry layer over which you will sprinkle cinnamon sugar, and cover with the final sheet.
8. Mark the circle on the pastry again and trim using a pastry cutter or a sharp knife (these offcuts will make a delicious bonus piece; sprinkle them with leftover cinnamon sugar and bake underneath the star). Place a small round pastry cutter or ring to mark the middle. Make 16 incisions up to the ring in the middle.
9. Now grab two adjacent pieces and twist them away from each other three times. Pinch the pastry together at the top. Continue with the other pieces until you shape all eight arms. Cover the star lightly with cling film and leave to prove for 40 minutes.
10. Preheat the oven to 170C (no fan)/340F/gas 3. Brush the risen star with beaten egg and sprinkle with pearl sugar if you like. Bake for 25-30 minutes until lightly golden.
11. Let the star cool on the tray for 10 minutes before transferring it carefully with the parchment on a wire rack. Dust with icing sugar or leave it golden and glistening for an impressive centrepiece!