Preheat the oven to 180°C/350°F/gas 4.
Lightly grease the bottom and sides of a 20cm springform cake tin with olive oil. Use scissors to cut out a circle of greaseproof paper, roughly the same size as the bottom of the tin, and use it to line the base.
Dust the sides of the tin lightly with flour, then tap the tin to get rid of any excess.
Break 200g of the chocolate into small pieces and add to a heatproof bowl.
Place the bowl on top of a small pan of simmering water over a medium heat, making sure the bottom of the bowl isn’t touching the water, and allow to melt, stirring occasionally.
Once melted, use oven gloves to carefully remove from the heat and put to one side – beware of the steam when you lift up the bowl.
Use a Y-shaped peeler to peel the beetroot (you might want to wear gloves to do this), then quarter them on a chopping board.
Push the beetroot through the coarse grater attachment on the food processor, then tip into a large mixing bowl.
Separate the eggs, placing the whites into a large clean mixing bowl and adding the yolks to the beetroot, then wash your hands.
Stir the sugar, almonds, baking powder, cocoa powder and melted chocolate into the beetroot and mix together well.
Use an electric hand whisk to whisk the egg whites until you have stiff peaks.
Use a spatula to fold a quarter of the egg whites into the beetroot mixture to loosen, then once combined, fold in the rest but try not to over-mix.
Add the mixture to the prepared cake tin and spread out evenly using a spatula.
Bake in the hot oven for around 50 minutes, or until risen and cooked through.
To check if it’s done, stick a cocktail stick or skewer into the middle of the sponge, remove it after 5 seconds and if it comes out clean the cake’s cooked; if it’s slightly sticky it needs a bit longer.
Allow the cake to cool slightly, then carefully turn it out on to a wire rack to cool completely.
When you’re ready to serve, melt the remaining chocolate (in the same way as above), then serve each slice with some yoghurt and a little drizzle of the melted chocolate.