Place the grated potato into a clean tea towel and wring well to get rid of excess moisture.
Heat the oil in a frying pan over a medium heat. Add the grated potato and chopped rosemary and season, to taste, with salt and freshly ground black pepper. Press down with a wooden spoon to make a cake shape.
Fry the rösti for 3-4 minutes, or until crisp and golden-brown, then dot the top with the lactose free butter.
Turn the rösti over and fry for a further 3-4 minutes, or until crisp and golden-brown. Remove from the pan and set aside to drain on kitchen paper.
To serve, cut the rosemary potato rösti into wedges and place them onto a serving plate.