Preheat oven to 170°C. Arrange 12-16 paper cupcake cases inside muffin tins.
Place chocolate and cocoa in a bowl. Melt butter in a small pot then pour onto chocolate and cocoa. Mix until chocolate has melted and mixture is well combined.
In a large bowl (or cake mixer), whisk eggs and caster sugar until thickened to custard consistency. Add melted chocolate mixture and stir until combined.
Sift the flour and baking soda into a medium bowl. Add one-third of this to the chocolate mixture and whisk until well combined. Then add one-third of the buttermilk and whisk well again. Repeat until you have no flour or buttermilk remaining.
Gently fold through the grated beetroot, stirring until just combined. Spoon mixture into the cupcake cases. Bake for about 18 minutes or until a skewer inserted into the middle of a cupcake comes out clean. Allow to cool for a few minutes, then transfer cupcakes to a wire rack to cool completely.
To make the whipped ganache, gently heat cream and chocolate in a bowl in the microwave or on the stove for 1-2 minutes, stirring often, until you have a smooth, silky ganache. Leave in the fridge to cool for about 1 hour. Once cold, use an electric beater to whip the ganache with the vanilla until smooth, fluffy and pale, much like a chocolate mousse (about 2 minutes).
Use a knife to top cupcakes with the whipped ganache. Decorate as desired.