Trim the leeks and wash them thoroughly. Cut into 1 inch lengths. Put the milk (or cream mixture) into a non-stick saucepan with the leeks and bring to the boil. If you like your leeks soft rather than slightly crisp, let them boil for a minute or two. Remove the leeks (leaving the milk in the pan) and put them into a baking dish. Put the eggs cold into boiling water and cook for exactly five minutes. Remove, cool and shell. The eggs should be soft in the middle but the whites will be firm. Lay the shelled eggs on the leeks. Make a white sauce by whisking in the cornflour, salt and butter and bring gently to the boil while you whisk. When the sauce is smooth, thick and glossy, pour it over the eggs and leeks, sprinkle the top with nutmeg and grated cheese and put it under the grill until it is hot and bubbling. Don't leave it too long or the eggs will be over-cooked. Serve at once with lots of crusty bread and butter.
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