Method:

1. Prepare the dough by whisking the milk, yeast, and 1 tsp of the caster sugar together. Let the mixture sit for 10-15 minutes until foamy. Add the egg yolks and vanilla to the yeast mixture. Stir well to combine.
2. Add the yeast mixture, flour, butter, salt, and remaining sugar to the bowl of your stand mixer. Attach the dough hook to the mixer and start on low speed, working up to medium speed to combine the dough. Knead for 5-10 minutes until the dough is soft and elastic.
3. Place the dough in a large, lightly greased mixing bowl. Cover with plastic wrap or a clean kitchen towel and allow the dough to rise in a warm, draft-free environment for 1-2 hours, or until doubled in size.
4. Meanwhile, prepare the custard by whisking the sugar, salt, and cornflour together. Beat the egg yolks in a medium-sized mixing bowl just until smooth. Add the dry mixture to the egg yolks and continue to beat until combined and pale yellow for about 1 minute.
5. Heat the milk in a saucepan over medium-high heat until it comes to a bare simmer. Remove the pan from the heat and carefully ladle the milk into the egg yolk mixture while whisking to avoid lumps. Pour the mixture back into the saucepan, and return it to the stovetop over medium heat.
6. While continuously whisking, heat the mixture until bubbling and completely thickened. Remove the pot from the heat. Whisk the vanilla and butter into the custard until smooth, then transfer the custard to a bowl.
7. Cover the custard with plastic wrap, carefully pressing the plastic directly against the surface of the custard to avoid a skin forming. Refrigerate for 1-2 hours or until completely cooled.
8. When the dough has risen, remove it from the mixing bowl. Punch the risen dough down and turn it out onto a lightly floured surface. Roll the dough out until about 1/2″ thick.
9. Use a 3″ biscuit or cookie cutter to cut rounds from the dough. Knead the remaining dough back into a ball and continue to roll it out and cut rounds until you’ve used as much dough as you can.
10. Place the rounds on a lightly greased baking sheet, leaving about 1″ of room between each round. Cover with plastic wrap or a clean kitchen towel and allow them to rise for 20-30 minutes, or until doubled in size.
11. Heat the oil in a large pot to 180c. Carefully place the rounds into the hot oil, working in batches. Cook for 1-2 minutes, or until golden brown, flip and cook for another minute or until golden. Remove the rounds with a slotted spoon and allow the donuts to drain on a paper towel-lined plate while you fry the rest.
12. Add the custard to a piping bag fitted with a piping tip. Insert a skewer or chopstick into each donut to create a pocket inside for the custard. Insert the tip of your piping bag into a donut and fill with custard. Repeat with the remaining donuts and custard.
13. Add the sugar and water for the caramel (brûlée) to a small saucepan over medium-high heat. Once the mixture starts bubbling, reduce the heat to medium. Heat the sugar, giving the pan a gentle swirl occasionally, until it turns golden. Take the pan off the heat and swirl the pan until the color deepens slightly.
14. Working very carefully, dip the top of each donut into the caramel. Wear a glove for extra protection on your hands. Lift the donut from the caramel and tilt it, away from your fingers, to let the excess drip for a few seconds, then place the donut aside to let it cool.
15. Repeat with the remaining donuts. If you find the caramel in the pot is getting too stiff, return it to the heat, swirling the pan, until it warms up and becomes less viscous.
16. Top donuts with salt.