In a medium saucepan, whisk together the chocolate milk, 70 g sugar, 1 tbsp cocoa powder, and cornstarch until smooth before turning on the heat.
Place the pan over low to medium heat and cook, stirring constantly, until the custard thickens and starts to bubble.
Once bubbling, reduce the heat to low and let it cook for 2 to 3 minutes while stirring, until very thick and smooth.
Remove the pan from the heat and let the custard sit for 1 minute.
Add the butter, 1 tsp vanilla bean paste, 1/4 tsp salt, and chopped dark chocolate to the hot custard and stir until fully melted and glossy.
Transfer the custard to a bowl and press plastic wrap directly onto the surface to prevent a skin.
Refrigerate the custard for 2 to 3 hours, or until completely cold and firm.
When ready to bake, preheat the oven to 350°F (175°C).
Grease and line two 8 inch round cake pans with parchment paper on the bottom.
In a small bowl or measuring jug, stir together 240 ml milk and vinegar and let sit for 5 minutes until slightly curdled.
In a large mixing bowl, whisk the 300 g sugar, 2 tsp vanilla bean paste, and vegetable oil until the mixture looks slightly thick and combined.
Whisk the milk and vinegar mixture into the sugar and oil until smooth.
Sift the flour, 60 g cocoa powder, baking soda, baking powder, and 1/2 tsp salt over the wet ingredients.
Whisk just until no dry streaks remain, then pour in the boiling water or hot coffee and whisk until the batter is smooth and pourable.
Divide the batter evenly between the prepared cake pans.
Bake for 25 to 30 minutes, or until the tops spring back lightly and a toothpick inserted in the center comes out with a few moist crumbs.
Cool the cakes in the pans on a wire rack for 10 minutes, then turn them out of the pans and let cool completely on the rack.
Once the custard is fully chilled, beat it briefly with an electric mixer or in a food processor until smooth and spreadable, stopping as soon as it looks creamy.
Place a small spoonful of custard in the center of your serving plate or cake stand to anchor the cake.
Set one cake layer on the plate, top side up.
Scoop 6 to 7 generous scoops of custard onto the first cake layer and spread it evenly to the edges.
Gently place the second cake layer on top, bottom side down, and align the edges.
Spread a thin layer of custard over the top and sides of the cake to create a crumb coat, then refrigerate for 30 minutes.
After chilling, apply the remaining custard over the top and sides of the cake and smooth it with an offset spatula.
Refrigerate the assembled cake for at least 30 minutes to allow the custard to set.
Before serving, let the cake sit at room temperature for 10 to 15 minutes for the best texture and flavor.