For the zucchini/courgette rösti, generously season the grated potatoes and then mix with the zucchini/courgette. Shape the mixture into flat patties, then cover and chill for 20 minutes.
In a frying pan, heat the oil over a medium heat. Fry the rösti for four minutes each side, or until crisp and golden-brown. Drain on a plate kitchen paper and keep warm until ready to serve.
For the poached egg, heat a pan of water to a very gentle simmer (the water should be just trembling and there should be a few bubbles rising up from the bottom of the pan).
Add the vinegar, break in the eggs and poach for three minutes. Lift out with a slotted spoon and drain briefly on kitchen paper. To serve, place a rösti in the centre of each plate and top with the poached eggs.