Trim and slice the leeks, rinse well, and drain.
Heat the oil in a large soup pot and sauté the leeks with salt and pepper until soft, about 10 minutes.
Add about 3 cups/750 ml water, slap the lid back on, and cook until are tender, about 15 minutes.
Add the spinach, peas and lettuce and let wilt into the liquid.
Purée with an immersion blender.
Press through a food mill into a clean saucepan.
Reheat, boiling down the soup a bit if it is too watery, or adding water if it is too thick.
Stir in the cream or milk, to desired consistency.
Serve with chopped fresh mint and a squirt of lemon juice to taste.
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