1 tablespoon unsalted butter
1 medium leek, roots removed, halved lengthwise, and thinly sliced
2 teaspoons kosher salt, plus more as needed
1/8 teaspoon freshly ground black pepper, plus more as needed
2 1/2 cups homemade vegetable broth or 1 cup low-sodium, store-bought vegetable broth mixed with 1 1/2 cups water
3 cups shelled fresh peas (from about 2 1/2 pounds of peas in their pods) or one 16-ounce package frozen peas, thawed
1/4 cup loosely packed fresh mint leaves
1 teaspoon freshly squeezed lemon juice, plus more as needed
Sour cream or Greek yogurt (optional)
Melt the butter in a medium saucepan over medium heat until foaming. Add the leek, 1/2 teaspoon of the salt, and a pinch of pepper and cook, stirring occasionally, until softened, about 3 minutes.
Add the broth, remaining 1 1/2 teaspoons salt, and measured pepper and bring to a boil. Add the peas and bring to a boil again. Reduce the heat to medium low and simmer until the peas are tender, about 5 minutes.
Remove the pan from the heat, add the mint leaves, and stir to combine. Let sit uncovered until the flavors meld, about 10 minutes.
Using a blender, purée the soup in batches until smooth, removing the small cap from the blender lid (the pour lid) and covering the space with a kitchen towel (this allows steam to escape and prevents the lid from popping off). Transfer the soup to a clean saucepan (if serving warm) or a heatproof bowl and stir in the lemon juice. Taste and season with more salt, pepper, and lemon juice as needed. If serving warm, reheat over low heat. If serving cold, let cool to room temperature, cover, then refrigerate until cold. Top each serving with a dollop of sour cream, if desired.