For the rösti, place the grated carrot, potato and courgette into a clean tea towel and squeeze the excess moisture out.
Heat the butter in a small frying pan, add the mixed grated vegetables, season, to taste, with salt and freshly ground black pepper and fry for 3-4 minutes each side or until golden-brown and crisp. Slide onto a serving plate.
For the beef, heat the vegetable oil in a pan, add the sliced steak and onion and fry over a high heat for 1-2 minutes.
Add the garlic, turn down the heat and cook for one minute.
Add the wine and thyme, season, to taste, with salt and freshly ground black pepper and bubble until the wine has reduced by half. Stir in the chopped parsley.
To serve, place the beef on top of the rösti and pour over the red wine sauce.