Grate the beetroot into a metal bowl.
Dry fry the fennel seeds in a pan and grind to a powder in a spice grinder. Mix with the vinegar, sugar, garlic, ginger and chilli.
Boil together for 20 minutes, and pour over the grated beetroot. Allow to cool. Boil the potatoes in their skins until soft, allow to cool slightly and peel.
Crush the potatoes with a fork and add the wasabi, horseradish, yolks and chives, mix well and season.
Heat a non-stick frying pan and lightly oil it. Spoon mixture into 4 oiled egg rings and cook over a moderate heat until golden brown, turn over and repeat.
Heat a grill pan, brush the beef fillets with a little oil and cook for 3-4 minutes on each side and allow to rest in a warm place.
Place a potato cake onto a warm dinner plate; slice the beef and place on top. Spoon the beetroot mix on top and drizzle some of the juice all around and serve.