Melt 3 tablespoons of the butter in a Dutch oven or large soup pot over medium flame. Add the leek and cook, stirring frequently, until it is soft and translucent, about 7 minutes. Don’t let it brown—reduce heat, if needed. Add garlic and cook another 2 minutes, stirring frequently. Add lettuce and cook, stirring frequently, until it wilts, another 7 minutes.
Add peas, stock, 1 cup of water, remaining 2 tablespoons of butter, and the salt and pepper, and bring to a simmer. Cook for about 5 minutes, until peas are soft. Using a slotted spoon, transfer about 1/2 cup of the peas to a small bowl and reserve (honestly, this was probably the most painstaking part of cooking this soup).
Stir in the tarragon and cream. Purée the soup until smooth, using a blender and working in batches. (Clark says you can also use an immersion blender, but that didn’t get it as smooth as we wanted it to be—use a blender.) Then return it to the pot. Taste and adjust the seasoning with salt, if needed.
If you’re making the ricotta topping, fold together the ricotta, the lemon zest and a little salt in a medium bowl; we found this took some serious stirring to soften the ricotta.
If you’re serving the soup warm, ladle it into individual soup bowls. Top with a dollop of the ricotta, a sprinkling of the whole peas and some chopped tarragon. Serve.
If you’re serving it chilled, refrigerate for 3 to 4 hours. Ladle into individual soup bowls and top with whole peas and tarragon. Serve.