In a medium saucepan, combine the sugar, cocoa, cornstarch, and espresso powder. Slowly stream in the chocolate milk while whisking.

Cook the custard mixture on medium heat while whisking continuously until it thickens and starts to bubble, about 10 minutes.

Strain the mixture with a sieve, then stir in the vanilla extract and butter. Press plastic wrap directly on the top of the custard and refrigerate until completely cool.

In a small saucepan, add the milk and butter and heat on low until the mixture reaches at least 90°F, but don’t let it get above 110°F. Add this mixture to the bowl of a stand mixer fitted with a dough hook attachment. Stir in the yeast.

Add the flour, sugar, salt, and egg to the bowl. Mix on low speed until the dough comes together, then scrape down the sides. Increase to medium speed and continue mixing for 5 minutes. Scrape down the bottom and sides of the bowl and continue mixing for another 1-2 minutes, until smooth and slightly sticky.

Form the dough into a ball and place it in a lightly greased bowl. Cover with plastic wrap and allow it to rise in a warm spot until doubled in size, about 1 hour.

Once the dough is ready, press out excess air and place it onto a lightly floured surface. Portion into 8 equal pieces and roll each into a tight ball. Place on a baking sheet lined with parchment paper and flatten each ball. Loosely cover with plastic wrap and allow to rest until slightly puffy, about 30 minutes.

Fill a medium heavy-bottomed pot with neutral oil, ensuring it is at least 2” deep. Heat the oil until the temperature reaches 350°F – 355°F, then reduce heat to maintain temperature. Place granulated sugar in a bowl for tossing.

Carefully place two donuts at a time in the heated oil. Fry for about 2 minutes per side until golden brown, ensuring the internal temperature is at least 190°F. Remove from oil using a slotted spoon and transfer to a sheet pan lined with paper towels.

Once all donuts are fried, toss them in the sugar until fully coated. Make a slit in the end of each donut to create a pocket for the custard.

Place the cooled chocolate custard in a piping bag fitted with a round pastry tip. Pipe the custard into the slit of each donut, then finish with a sprinkle of chocolate shavings and enjoy!