Make the pastry cream by heating the milk and vanilla in a medium pot to just shy of a simmer. It is difficult to tell when milk is simmering, so I just bring it to about 195-200 degrees F. 

Whisk together the egg yolks, sugar, and cornstarch. Once the milk is hot enough, pour half of it into the egg mixture, whisking constantly to temper them. Whisk for another minute and then pour all of it back into the pot and heat over medium heat, whisking constantly. Once the pastry cream thickens and the bubbles disappear, continue whisking for one more minute and then remove from heat.

Transfer the pastry cream to a small bowl and whisk in the butter one tablespoon at a time. Cover with plastic wrap, pressing it against the surface, so a skin does not form and place in the fridge to cool overnight.

Line a baking sheet or pan with aluminum foil and grease with butter.

In a medium saucepan, heat the sugar and water over medium heat, stirring occasionally until the sugar dissolves. Once it starts bubbling, increase the heat to medium-high and only swirl it, do not stir it. Heat for about 10 minutes, or until it turns an amber color. 

Remove from heat and quickly whisk in baking soda. Pour over the prepared pan (do not spread with spoon or spatula, as this will deflate the bubbles). Allow to cool completely before breaking into pieces. 

Heat the milk to 110 degrees F and stir in yeast and sugar. If using active dry yeast, allow to sit for 15 minutes. If using instant yeast, simply move on to the next step.

Mix the eggs and vanilla into the milk yeast mixture.

Combine flour, malted milk powder, and salt together in the bowl of a stand mixer fitted with a dough hook. Pour the wet ingredients into the flour and mix on low-medium speed for about 3 minutes, or until it forms a ball around the hook.

Add in one piece of butter at a time, allowing it to fully incorporate before adding the next. Once all of the butter is incorporated, turn the mixer up to medium-high speed and mix for 6-8 minutes. To check if the dough is ready, tear off a small piece and carefully spread it out to see if you can see the light through it without it tearing. If it tears, mix for another minute and check again.

Once the dough is ready, transfer it to a lightly greased bowl, cover, and allow to proof overnight in the fridge.

Divide the dough into 8 equal pieces and roll into smooth balls. Allow the donuts to proof at room temperature for 30 minutes.

While the donuts proof, pour enough vegetable oil in a cast iron pot to fill two inches and heat to 350-360 degrees F.

Fry the donuts, two or three at a time, for 30 seconds on each side for a total of 2-3 minutes. Dry donuts off on paper towels quickly and then transfer to a cooling rack over a baking sheet. Allow to cool completely before filling.

Grind up about 50g of the burnt sugar in a blender. Transfer to a small bowl and coat each donut in the sugar. 

Using a skewer or the end of silverware, poke a hole in each donut. 

Mix about half of the burnt sugar pieces (or more if desired) in the pastry cream and transfer to a piping bag with a medium round tip. Pipe cream into each donut and top with bigger burnt sugar pieces.