Put the potatoes in a large pan of water and bring to the boil. Boil for about 20 minutes until the potatoes are just cooked but firm. Drain and cool.
Peel the potatoes and grate them into a bowl. Stir in the grated Cheddar and onion. With wet hands, shape into 4 rounds, then press down with 2 fingers to form into röstis. Neaten up the edges.
Brush lightly with oil on both sides and grill on a foil-lined grill rack at a medium heat for 2–3 minutes on each side until golden brown.
Serve the röstis warm with the ketchup. (Any that are not needed straight away may be stored in an airtight container in the refrigerator for up to 3 days.)