Trim off stem end of each leek. Cut off enough of the green part to leave a main section of about seven inches. Split the leeks lengthwise in half. Cut the split leeks crosswise into 1-1/2” lengths. There should be about 8 cups loosely packed. Rinse thoroughly in cold water. Drain.
Put the leeks into a heavy skillet and add the butter, salt and pepper to taste and the nutmeg. Cook, stirring about one minute. Add the cream and bring to a simmer. Cover and cook 15 minutes until tender.
Preheat broiler
Spoon the hot leeks into a baking/serving dish and smooth the top. Sprinkle the top with cheese and place under the broiler until cheese browns and is nicely glazed. Serve hot.