Cut the leeks in half lengthways, then into chunks. Rinse well and drain.
Heat the oil in a frying pan and sauté the leeks. Cover and reduce over a low heat until the leeks have melted. Finish cooking, uncovered, to remove any residual moisture. Season with salt and pepper.
Heat the water and milk in a saucepan. When it comes to the boil, add ½ tsp salt and then pour in the polenta, stirring well. Leave to thicken for 2 to 3 minutes over a low heat, stirring constantly.
Without waiting, pour half the polenta into an oiled gratin dish. Arrange the leeks on top of the polenta, followed by thin slices of Fourme d'Ambert cheese. Cover with the remaining polenta. Even out the surface and sprinkle with a few small pieces of butter and a few cubes of Fourme cheese.
Bake for approximately 30 to 45 minutes at 180°C. Leave to cool for 10 mins before serving, perhaps accompanied by a salad.