Equipment and preparation: You will need an ice cream maker.
For the ice cream, fry the sliced onions in the butter very gently until soft but not coloured. Cool slightly, transfer to a food processor and blend to a purée.
Heat the milk and sugar in a saucepan, stirring to dissolve, until it just comes to the boil.
Combine the hot milk, onion purée and the cream, then set aside to cool.
Chill in the fridge until cold, then churn the mixture in an ice cream machine. Transfer to the freezer to firm up.
For the beef fillet, preheat the oven to its lowest temperature – ideally, 60C/140F.
Heat the oil in a frying pan until very hot. Season the beef with salt and freshly ground black pepper. Sear the beef, then remove from the pan and wrap in heatproof cling film.
Place the wrapped fillet on a tray and roast for about 55 minutes, turning halfway through cooking. Using a meat thermometer, check the temperature of the beef is 50C/120F. If not, turn up the heat in the oven a little and put the beef back in for 8-10 minutes. Keep doing this until the temperature reaches 50C/120F. Then set the beef aside to rest.
For the potato purée, place the whole potatoes in a large saucepan with enough salted, cold water to cover. Bring to the boil and simmer for 25-30 minutes until soft. While still hot, remove the skin and pass through a sieve or ricer.
Bring the double cream to the boil in a small saucepan and then strain through a sieve.
Stir the hot cream and butter into the potatoes, add salt and freshly ground black pepper to taste, and stir in the horseradish cream. Pass through a sieve again and keep warm until serving.
For the jus, heat the olive oil in a large saucepan and fry the beef trimmings until well browned. Add the shallots, garlic, thyme, bay leaf, salt and black pepper, and cook until golden-brown.
Add the port and cook until it has completely evaporated, then add the red wine and boil until the volume of the liquid is reduced by two-thirds.
Add the stock and boil until the sauce has reduced by two-thirds again.
Strain through a fine sieve into a clean pan and reheat gently, then whisk in the butter a little at a time.
For the carrots, scrub the carrots and blanch in salted water until just tender. Refresh in iced water and drain.
Cook the carrots in butter in a frying pan over a medium heat until carmelised and golden-brown, seasoning to taste with salt and freshly ground black pepper.
For the bone marrow persillade, scrape the marrow out of the beef and chill in the fridge. When hardened, chop the marrow finely.
Heat the butter in a pan over a medium heat until foaming and golden-brown. Remove the pan from the heat and add the breadcrumbs, chopped bone marrow and parsley. Set aside.
To serve, spoon some potato purée onto the centre of each of four serving plates. Slice the beef, and place on top of the purée. Drizzle a couple of tablespoons of the jus on top and around the beef. Place three carrots of different colours on top of the beef, and sprinkle the persillade on top. Place a dab of potato on the other side of the plate and sit a scoop of ice cream on top.
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