Preheat the oven to 225C/450F/Gas 7.
For the sauce, place the carrot, butter and shallot into a saucepan, over a medium heat and let it cook gently for five minutes.
Add the wine, garlic and stock and simmer for a further five minutes.
Add the cream and let it boil for two minutes to thicken the sauce.
Meanwhile, make the rösti, by mixing together the carrot, potato, flour and horseradish in a bowl and season with sea salt and freshly ground black pepper.
Heat the oil in a small ovenproof frying pan and when hot, add all the rösti mixture, gently pressing down. Cook for five minutes, then transfer to the oven for a further five minutes to finish cooking.
For the beef, heat the oil in a pan. Season the steak on both sides and add to the pan to fry for a minute on each side, or until cooked to your liking.
To serve, strain the sauce and spoon around the plate. Add the rösti and then place the steak on top.