Make the Pastry Cream: In a medium saucepan, gently heat the milk and vanilla bean paste until it's steaming but not boiling. While it heats, whisk the egg yolks, caster sugar, and cornflour together in a mixing bowl until pale and smooth.

Temper the Eggs: Once the milk is hot, slowly pour about half of it into the egg yolk mixture while whisking constantly. This is called tempering and prevents the eggs from scrambling. Pour the tempered egg mixture back into the saucepan with the remaining milk.

Thicken and Chill the Cream: Return the saucepan to a medium heat and cook, whisking continuously, for 3-5 minutes until the cream thickens significantly and a few bubbles burst on the surface. Remove from the heat and whisk in the cold, cubed butter until it has melted completely. Pour the cream into a shallow dish, press a piece of cling film directly onto the surface to prevent a skin from forming, and refrigerate for at least 2 hours, or until completely cold.

Prepare the Donut Dough: In a large bowl or the bowl of a stand mixer, combine the lukewarm milk, yeast, and a pinch of the sugar. Let it stand for 5-10 minutes until it becomes foamy. Add the remaining sugar, eggs, and melted butter, and mix to combine. Add the flour and salt.

Knead and Prove the Dough: Using a dough hook, knead on a medium-low speed for 8-10 minutes (or knead by hand on a lightly floured surface for 10-12 minutes) until the dough is smooth, soft, and elastic. Place the dough in a lightly oiled bowl, cover with a clean tea towel, and leave to rise in a warm place for 1 to 1.5 hours, or until it has doubled in size.

Shape and Second Prove: Gently knock the air out of the dough on a floured surface and roll it out to about 1.5cm (just over half an inch) thickness. Use an 8cm (3-inch) round cutter to cut out as many circles as you can. Place the donuts on a floured baking tray, cover loosely, and let them prove for another 30-45 minutes until they look puffy.

Fry the Donuts: Heat the oil in a large, heavy-bottomed pan or deep-fryer to 180°C (350°F). A kitchen thermometer is essential here. Carefully fry the donuts in batches of 2-3 at a time for about 60-90 seconds per side, until they are a deep golden brown. I find that using two chopsticks or a spider strainer is the best way to flip them without splashing. Remove with a slotted spoon and place on a wire rack to cool completely.

Make the Frosting: While the donuts cool, melt the dark chocolate, butter, and golden syrup together in a heatproof bowl set over a pan of simmering water (or in the microwave in short bursts). Whisk until smooth, then stir in the milk or cream to get a pourable consistency.

Fill and Glaze: Once the donuts are cool and the cream is chilled, give the cream a good whisk to loosen it up and transfer it to a piping bag fitted with a plain nozzle. Use a small, sharp knife to make a hole in the side of each donut, wiggling it to create a pocket inside. Pipe the pastry cream into each donut until it feels full. Dip the top of each filled donut into the chocolate frosting, letting any excess drip off. Place back on the wire rack for the frosting to set.