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Melt the butter in a frying pan and add the sliced leeks.
Cook on low for 5 minutes until the leeks are softened.
Add the eggs and milk to a jug or bowl along with some salt and pepper and whisk with a fork.
Pour this into the frying pan and add the grated cheese on top.
Cook on low for 3 minutes until the bottom of the omelette has browned.
Transfer to under the grill for another 1-2 minutes until the cheese has completely melted.
Serve immediately.