Combine all of the stock ingredients in a large pot. Bring to a boil, reduce the heat to medium, and simmer, partly covered, 20-30 minutes. Strain and reserve the stock. (If you're like us, pull out all the carrots and potato chunks and mash them up with a knob of butter and some salt for a pre-soup snack.)
Make the soup:
Meanwhile, place the sliced leeks in a large bowl and fill with cool tap water. Swish the leeks occasionally to remove any sand from between their layers, which will sink to the bottom. Melt the butter in a large saucepan over medium heat. Lift the leeks out of the water, give them a shake, and add them to the pot along with the diced potato. Saute, stirring frequently, until the leeks are tender, 10 minutes, reducing the heat if the leeks begin to brown at all. Add 6 cups of the stock and the salt, bring to a simmer, and cook until the potatoes are tender, 10 minutes or so. Add the peas, and simmer 5 minutes. Add the lettuce, and bring to a simmer for 1 minute. Remove from heat and let cool to room temperature.
Add the mint leaves, and puree the soup with a hand blender or in batches in a blender. Add the lemon juice. Taste, adjusting the salt or lemon if needed, adding more stock or water to thin the soup if you like.
To serve, heat the soup gently, stirring frequently, over a medium flame until just warm. Ladle into bowls, and swirl with crème fraîche, peas, a few mint leaves, and a handful of croutons.
The soup is best shortly after being made when the color and flavor are bright, but it will keep, refrigerated, for up to 5 days.
Notes
Adapted from Epicurious.I won't lie; I use a combination of fresh and frozen peas for this soup. Be sure you're buying English peas, the kind designed for shelling. As you prep your soup ingredients, add the trimmings to the pot.For the best color and flavor, let the soup cool to room temperature before adding the mint and lemon juice and pureeing. Reheat gently to keep the fresh flavor of the mint and lemon.I like this soup best barely warm, swirled with crème fraîche, a handful of fresh peas, and some crunchy croutons.Nutritional values are based on one of six servings.