For the rösti, preheat the oven to 180C/350F/Gas 4. Using a coarse grater, grate the pumpkin and potato into a large bowl. Add the red chillies and the coriander and season with salt and freshly ground black pepper.
Remove the excess liquid from the pumpkin mixture by squeezing it in a clean tea towel over the sink. Divide the mixture into four equal patties and shape to make the röstis.
Heat the oil over a medium heat in a large frying pan. Carefully place the patties into the pan and fry on both sides for about three minutes ,or until golden-brown. Transfer to a baking tray and place in oven for 15 minutes, or until fully cooked through.