Put the grated potatoes in a tea towel and wring out as much liquid as you can. Transfer to a large bowl with the parsnips, onion, sage and a tablespoon of oil. Season well and mix together with your hands.
Put your largest nonstick frying pan on a medium heat, add a few knobs of the butter and a splash of oil – you will need to cook the rösti in batches, so turn on the oven to low to keep the cooked ones warm.
When the fat is hot and sizzling, add small handfuls of the potato mix, then flatten them down with a wooden spoon and shape into rounds. Add extra butter or oil to the pan if it looks dry.
Fry for five to six minutes on each side, very carefully turning them over with a spatula when golden underneath. Depending on the size of the röstis, you should end up with 10 to 12.