Preheat the oven to 200C/400F/Gas 6.
For the seared beef, season the beef fillet with salt and freshly ground black pepper and drizzle with olive oil.
Heat a griddle pan until smoking hot and sear the beef for two minutes on both sides. Remove from the heat and leave to rest for five minutes.
For the red wine and shallot sauce, heat most of the butter in an ovenproof frying pan. Add the shallot halves and a pinch of the sugar and stir.
Transfer to the oven and roast for ten minutes.
Remove from the oven and return to the hob. Add the wine to the pan and simmer for 1-2 minutes.
Add the stock, the remaining sugar and the remaining small knob of butter and season well with salt and freshly ground black pepper. Simmer for 3-4 minutes, then set aside in a warm place.
For the rösti potato, heat the olive oil in a small frying pan. Place the grated potato into a clean tea towel and squeeze out the excess water. Place the grated potato into a bowl with the thyme, salt and freshly ground black pepper, and mix well.
Place the potato mixture into the frying pan and press down. Fry for 3-4 minutes, then turn over and fry on the other side for 3-4 minutes. Towards the end of the cooking time, push a little butter down the edges of the rösti to add flavour and help to make it crisp and golden-brown. Remove from the pan, drain on kitchen paper and then slice into four pieces.
For the carrots, place the halved carrots into a small saucepan with the butter, sugar and a splash of boiling water. Cover with a lid and cook for five minutes, shaking the pan from time to time, until the carrots are tender.
To serve, place the seared beef onto a plate. Pile the potato rösti and glazed carrots alongside and pour over the red wine and shallot sauce.