Peel and wash the potatoes.
Grate and season with salt and pepper.
Squeeze well to remove excess liquid.
Heat the oil in a large non-stick pan. Add a quarter of the potatoes and press flat. Cook over a low heat until the rösti is lightly browned underneat, then turn and brown on the other side as well.
Transfer the rösti to a baking tray lined with baking paper. Make 3 more rösti using the remaining potatoes.
Wash the tomatoes, slice them and arrange on the rösti. Cover with basil.
Sprinkle with the cheese.
Bake in the oven at 220°C (200°C fan, gas 7) for 10-15 minutes until lightly browned.