I would advise you to wear fine latex gloves when preparing the beetroot - otherwise your hands will be quite stained.
Dice the beetroot, cooked carrot and apple. Put all these into a medium-sized bowl. Chop the onion finely. Cut the celery into small pieces. Add these to mixture and stir to allow the flavours to develop.
Allow the salad to stand for at least one hour before serving.
For the dressing, melt the butter in non-stick saucepan. Beat egg, vinegar, mustard, sugar and salt and add to pan. Heat very gently, stirring all the time until custard-like. Allow to cool. Add cream or milk to salad dressing before serving. The dressing should be like thick cream. The dressing can be kept in the fridge for one week.