Preheat oven (electric cooker: 180 °C/circulating air: 160 °C/gas: see manufacturer). Oil a box mould (approx. 11 x 25 cm; 1 3⁄4 l capacity). Place a strip of baking paper (approx. 20 x 40 cm) in the baking tin so that the narrow sides remain free. Clean, peel and roughly grate the beetroot. Separate the eggs.
For the dough, beat the egg whites until stiff, set aside. Mix 180 ml oil and sugar with the whisks of the mixer, add egg yolks one after the other. Mix flour, baking powder, cocoa and 1 pinch of salt. Sieve onto the sugar-oil-mix, stir in briefly. Mix in beetroot and almonds. Fold in the beaten egg white. Smooth in the mould. Bake in a hot oven for 1-1 1⁄4 hours.
Take the cake out of the oven. First cool in the mould for approx. 30 minutes, then carefully lift out and let it cool down. Meanwhile, for the cream, whisk butter and 160 g sieved icing sugar with the whisk of the mixer for approx. 4 minutes until white and creamy. Stir in cream cheese and beetroot juice by the spoonful.
Cut the cake horizontally twice. Place the lower cake base on a cake plate and spread approx. 1⁄3 cream on top. Place the middle cake layer on top and spread with 1⁄3 cream. Place the cake lid on top, spread with the rest of the cream and chill for about 30 minutes. Remove the pistachios from the shell and chop roughly. Mix 100 g icing sugar with lemon juice. Dribble in thin strips over the cake and sprinkle with pistachios.