Whilst the dough is chilling, you can prepare the white chocolate and tiramisu créme patissiere. Place the milk and roughly crushed coffee beans in a large saucepan. Use a sharp knife to horizontally split open the vanilla bean pod. Scrape the seeds into the saucepan then add in the split pod too. Heat the mixture over medium heat until it reaches a light rolling boil. Remove from the heat and let the mixture sit to infuse for 30 minutes.
With an electric hand whisk, whisk the yolks, sugar and cornflour in a medium sized bowl until pale, fluffy and leave the mixture leaves a trail when the whisk is gently lifted, about 3 minutes. Set the bowl aside.
Strain the milk mixture through a fine mesh sieve and discard the crushed coffee beans and vanilla bean pod. Re-weight the milk. The coffee beans would have absorbed about ¼ of the milk so add enough extra milk so that it reaches 500 millilitres (16.9 fluid ounces) again. Return it to the saucepan and heat, over medium-low, until it is just beginning to simmer.
Remove the mixture from the heat and ladle in a generous scoop of the milk into the egg yolk bowl. Whisk it vigorously to combine and acclimatise the eggs then return the mixture back into the saucepan with the milk. Set it back over the heat. Whisk often, concentrating whisking around the edges of the pan until the mixture is thick enough to coat the back of a spoon and leaves a trail.
Remove from the heat and whisk in the white chocolate until smooth and melted then whisk in the coffee liqueur or marsala.
Transfer the créme patissiere to a large bowl and cover the surface closely with a piece of plastic wrap. Refrigerate until cold, 3 hours.
Once cold, fold in the mascarpone and the finely chopped dark chocolate. Transfer the mixture to a piping bag fitted with a 2 centimetre (.8 inch) round nozzle. Refrigerate until required.
To make the doughnuts and coffee and vanilla bean sugar:
When you are ready to make the doughnuts, transfer the chilled dough onto a lightly floured work surface. Roll it out with a lightly floured rolling pin until it is about 28 centimetres (11 inches) wide and about .6 centimetres (1/4 inch) thick.
Using a 7.5 centimetre (3 inch) circular cutter cut out 8 dough circles. Carefully transfer them to a parchment lined baking tray or slipmat. Then, using a 2.5 centimetre (1 inch) circular cutter, cut out as many mini circles as you can with the scraps. Re-roll the remaining scraps by gently kneading the dough together to cut out more mini circles. Transfer them to the tray and cover it with a piece of plastic wrap. Place in a warm place to prove for a further 1 hour.
Meanwhile, make the coffee and vanilla bean sugar by blitzing the sugar, espresso powder and vanilla bean seeds in the bowl of a small food processor until fragrant and the espresso is evenly distributed throughout. Alternately, you can grind the ingredients together in a mortar and pestle. Set the sugar aside in a medium sized bowl.
When the doughnuts have risen, pour the oil into a large and deep saucepan. Heat, over a medium-low temperature until it reaches 175 C (350 F). Watch the temperature closely! The temperature should quicken as it nears close to 175C (350 F).
Gently pick a doughnut up and place it in the oil. Fry on one side for 2 minutes then flip with a handheld metal strainer and fry on the other side for a further 1 minute or until golden brown all over. Remove the doughnut and let it cool on a kitchen paper towel lined baking tray for about 5 minutes before transferring it into the bowl of sugar and generously coating it. Repeat with the remaining doughnuts, making sure not to fry more than 3 to 4 at a time.
When you are ready to fill the doughnuts, use a sharp knife to insert a little hole into the sides of each. Insert the piping nozzle into the hole and pipe in as much of the white chocolate and tiramisu créme patissiere as the doughnut allow, letting some of it ooze out of the sides. Repeat with the remaining doughnuts.