Mix all the dry ingredients (flour, cocoa and salt), in a bowl, keep aside.
Put the oil and sugar in the bowl, mix: 40 sec. speed. 4.
Add the eggs, one at a time, setting to speed 4, beating for 30 seconds after each addition.
Add the dye and vanilla, mix well: 20 sec. speed. 3.
Add the mixture with the flour alternating it with buttermilk twice: 1 min. speed 4.
Put the baking soda in a small bowl, pour over the vinegar and add the mixture to the mixture, mix: 20 sec. speed 4.
At this point, pour the resulting dough into a cake pan previously covered with parchment paper and bake in a preheated oven at 180 degrees for about 30-40 minutes (always do the toothpick test). Set aside and allow to cool completely.
Take the butter out of the fridge at least 20 minutes first and then put it in small pieces in the mug, whip up: 1 min. speed 4.
Add the cold cheese, whisk again: 1 min. speed. 4.
Add the vanilla extract and a pinch of salt, mix: 10 min. speed 4.
Then, with the blades moving at speed. 3, add the icing sugar a little at a time and whisk for another 2 minutes or until the mixture is smooth and creamy.
Refrigerate in a bowl covered with plastic wrap for at least 15-20 minutes before use (can be kept for up to 6 days in the refrigerator).
Take back the cooled cake and cut it into 2 equal discs. Fill each disc with the cheese frosting and cover the surface of the cake with the leftover one.
If you like, you can cut away some of the dough and crumble it on the surface.
Place for at least 1 hour covered by a glass bell in the refrigerator. Take it out half an hour before serving it... Enjoy your meal!
Buttermilk can be found in organic stores or specialized supermarkets, or you can prepare it following the recipe for the thermomix.