Preheat the oven to 200C/400F/Gas 6.
For the melting Brie rösti, place the grated potato into a clean tea towel and squeeze the liquid out. Remove the potato from the tea towel and season well with salt and freshly ground black pepper.
In a small ovenproof, non-stick frying pan, heat the butter and oil together and press in half of the grated potato to cover the base of the pan.
Place the sliced Brie on top of the potato and top with the remaining half of grated potato.
Fry the potato for two minutes on each side until golden-brown.
Transfer the pan to the oven for a further six minutes, or until the potato is tender.
For the sautéed steak, heat the olive oil in a non-stick frying pan and fry the steak on both sides until cooked to your liking. Leave to rest for five minutes.
To serve, place the rösti and green beans onto a serving plate with the steak.