In a medium pot, whisk together chocolate milk, cane sugar, cocoa powder, and cornstarch until smooth. Cook over medium heat, stirring constantly, until the mixture thickens—about 8-10 minutes. Once thickened, remove from heat and stir in unsalted butter, vanilla extract, salt, and dark chocolate until completely smooth. Transfer the custard to a bowl, cover, and refrigerate for 2-3 hours until set and chilled.

Preheat your oven to 350°F (175°C) and grease two 8-inch round cake pans, lining them with parchment paper for easy removal. In a bowl, mix room temperature milk with white vinegar and let it curdle for 5 minutes. Add vegetable oil, vanilla extract, and cane sugar, whisking until completely dissolved before continuing with the dry ingredients.

Sift together all-purpose flour, baking soda, baking powder, and a pinch of salt into the wet mixture. Stir until just combined, ensuring no lumps remain. Carefully add boiling water or fresh brewed coffee in small increments, mixing slowly until the batter is smooth and well combined.

Divide the batter evenly between the prepared cake pans, smoothing the tops with a spatula. Bake in the preheated oven for 25-30 minutes, or until a toothpick inserted into the center comes out clean. Once baked, remove the cakes from the oven and allow them to cool in the pans for about 10 minutes. Then, gently transfer them to wire racks to cool completely.

Once the cakes are completely cool, level the tops with a serrated knife if needed. Place one cake layer on a cake stand and generously spread a layer of chilled chocolate custard over the top. Carefully place the second layer on top and apply a thin crumb coat of custard all around the cake to lock in the crumbs; refrigerate the cake for 30 minutes to set the coat.

After chilling, spread a final, smooth layer of chocolate custard over the entire cake. For an added decorative touch, apply crumbled cake trimmings around the sides for texture. Refrigerate the assembled Chocolate Custard Cake for at least 30 minutes before serving to ensure everything is set and flavors meld beautifully.