Grease a 20 cm (8 inch) round deep cake tin.
Whisk together the melted butter and sugar in a large bowl until pale. Stir in the beetroot, two-thirds of the nuts and the egg yolks.
Stir together the baking powder, cinnamon, orange rind and juice, flour and ground almonds in a separate bowl. Add to the beetroot mixture and beat until smooth.
Whisk the egg whites in a large clean bowl until they form soft peaks, then fold into the beetroot mixture.
Spoon the mixture into the prepared tin and place in a preheated oven, 200°C (400°F), Gas Mark 6, for 45–50 minutes until firm to the touch. Remove from the oven and transfer to a wire rack to cool.
Beat together the cream cheese and icing sugar in a bowl, then smooth the icing over the top of the cooled cake. Decorate with the whole nuts.