Place the grated potato and parsnip onto a clean tea towel and squeeze over a bowl to remove the excess liquid.
Melt the butter with the oil in a frying pan over a medium heat, add the grated potato and parsnip, press down and season with salt and freshly ground black pepper.
Fry the rösti for 2-3 minutes on each side, using a fish slice to carefully turn it over, until crisp and golden-brown.
To serve, place the rösti onto a plate and sprinkle over the parsley.
