Prepare the pastry cream. 

1. Begin by heating the milk in a saucepan with sugar. Scrape the seeds from the vanilla bean and add both the seeds and the pod to the milk so you use every bit of flavor.
2. In a separate heatproof bowl, whisk together the eggs and cornstarch until completely smooth and free of lumps.
3. Once the milk mixture reaches a gentle boil, carefully ladle a full scoop into the egg mixture, whisking constantly to prevent the eggs from scrambling. Then, pour the combined mixture back into the saucepan.
4. Cook over low heat, stirring continuously, until the cream thickens to a smooth, pudding-like consistency. Remove from the heat, strain through a fine-mesh sieve to remove the vanilla pod and any cooked bits, and immediately cover the surface with plastic wrap to prevent a skin from forming. Chill until ready to use.

Prepare the donut dough. 

1. To make the dough, warm the milk until lukewarm, then stir in the yeast and 1 tablespoon of sugar. Let sit for 10–15 minutes until frothy.
2. In a large bowl or stand mixer, combine the flour, remaining sugar,  salt,  yeast mixture, egg, vanilla extract, and softened butter. Mix until a dough forms, then knead for 20 minutes until smooth and elastic.
3. Place the dough in a greased bowl, cover, and let rise in a warm place until doubled in size, about 1 hour and 45 minutes.
4. Gently punch down the dough and roll it out to 0.4 cm thick. Cut into rounds using a 7–8 cm cutter. Place on parchment-lined trays.
5. Cover and proof again for 45–60 minutes until puffy.
6. Heat oil to 175–180°C. Fry the donuts 2–3 at a time for 1–2 minutes per side until golden. Drain on a wire rack, but immidietly after cover in granualted sugar.

Finish: 

1. Once cool enough to handle, poke a hole in the side of each donut and pipe the chilled custard inside. Serve fresh.