Preheat the oven to 180C/350F/Gas 4.
Cook the potato in boiling water for 8-10 minutes, or until tender, then drain and mash with a potato masher or fork. Mix in the flour and milk and season, to taste, with salt and freshly ground black pepper.
Heat the olive oil in an ovenproof frying pan, shape the potato mixture into four patties and fry for 2-3 minutes on both sides, or until golden-brown and crisp. Place one slice of cheese over each potato patty and place into the oven to cook for 2-3 minutes, or until the cheese is melted and bubbling.