Bring plenty of salted water to the boil in a very large saucepan. Trim and wash the leeks, removing the tough, outer layer and the ends of the green leaves. Keep them whole but cut down into quarters from the top, green end to within about 3 in (7 cm) of the root end to enable you to wash them thoroughly. Boil for 20 minutes and drain.

Preheat the oven to 400°F (200°C) mark 6.

Bring the milk slowly to the boil in a small saucepan. Mix the cornflour or potato flour with 2 tbsp cold water and stir into the hot milk off the heat. Return to the heat and continue stirring for about 1/2 - 1 minute as the milk thickens. Remove from the heat and beat in the cream a little at a time using a balloon whisk. (This is not a thick sauce.) Season with salt, pepper and nutmeg.

Use a little of the butter to lightly grease a shallow ovenproof dish large enough to accommodate all the leeks. Slice the leeks across, cutting them in half. Arrange in a single layer in the greased dish alternating a green half with a white half. Cover with the white sauce. Sprinkle with the cheese and dot with flakes of the remaining butter; bake in the oven for 25 minutes and finish by placing under a very hot grill for 5 minutes to brown.

Serve at once.