First, prepare the coconut ganache. Finely chop the chocolate and place it in a heatproof bowl.
Heat the heavy cream until it is just below boiling point (do not let it come to a full boil), then pour it over the chocolate. Immediately add the coconut milk.
Let it sit for 1–2 minutes without stirring, then start mixing from the center outwards with slow motions until the chocolate is fully melted and you get a smooth, glossy cream. If there are still small pieces of chocolate, heat the bowl in the microwave for 20–30 seconds and stir again.
When the ganache is completely smooth, fold in the shredded coconut and, if you have it, the coconut paste for a more intense flavor. Cover the ganache “in contact” with plastic wrap (the wrap should touch the surface of the cream) and leave it at room temperature or in the fridge until it sets and reaches a creamy consistency.
For the chocolate sponge, beat the eggs with the sugar until they triple in volume and become pale in color. Gradually add the melted butter and the vegetable oil, mixing on low speed just until combined.
In a separate bowl, whisk together the dry ingredients: flour, baking soda, salt, and sifted cocoa powder. Add the dry mixture to the egg mixture in 2–3 additions, folding gently with a spatula or mixing on the lowest speed just until no streaks of flour remain.
Pour in the milk, vanilla, and vinegar, mixing continuously but gently so the batter stays airy and smooth, without lumps. Do not overmix, so you don’t lose the volume.
Line two springform pans or a cake ring with parchment paper on the bottom, divide the batter evenly between them, and smooth the tops. Bake at 350 °F (180°C) in a preheated oven until the layers pass the toothpick test and spring back lightly when pressed.
After baking, let the cake layers cool in the pans, then remove them, wrap each one tightly in plastic wrap, and chill for at least 2 hours in the fridge, preferably overnight, so they firm up and are easier to slice.
For assembly, if you want a moister cake, prepare a simple vanilla sugar syrup and lightly soak the cooled layers; if you prefer a classic chocolate sponge texture, you can skip this step.
Assemble the cake in an adjustable ring or springform pan: place the first layer, spread an even layer of coconut ganache on top, then set the second layer over it, pressing gently. Chill the cake for at least 4 hours, until the ganache is firm and the cake is well set in the pan.
Carefully remove the ring, trim the edges if needed, and decorate the cake with melted chocolate. For a nice shine, stir a small amount of neutral-tasting vegetable oil (for example, grapeseed oil) into the melted chocolate until it becomes fluid and glossy, then pour it over the top of the cake.