Pour olive oil into a large pot, set over medium heat. Add leeks to hot oil, season with a pinch of salt.
Cook, stirring often, until leeks are soft, 5 to 6 minutes. Pour chicken broth into pot with leeks; bring to a boil. Season with black pepper and cayenne pepper.
Stir peas into boiling broth mixture and add two mint leaves. Bring back to a boil and cook until peas are bright green and have started to soften, about 5-6 minutes.
Turn off heat. Use a slotted spoon to transfer vegetables into a large blender, leaving liquid in pot. Pour half the liquid from the pot into the blender, place a folded towel on the blender lid, and pulse a few times to chop vegetables. Blend at high speed to puree vegetables. Add remaining liquid from pot to blender and liquify the soup until smooth.
Pour soup from blender into a fine mesh strainger set over a bowl and use a spatula to push soup through the strainer, leaving the tough fibrous material behind.
Cool soup to room temperature, cover with plastic wrap, and refrigerate until thoroughly chilled, about 3 hours.
Season cold soup with salt and cayenne pepper. Ladle soup into a serving bowl. Spoon creme fraiche over the top of the soup in a loose spiral. Use a skewer to adjust spiral shape if desired. Cut remaining two mint leaves into strips for garnish and serve.
Bring a large pot of lightly salted water to a boil. Add linguini pasta, and cook for 8 to 10 minutes or until al dente. Drain, reserving 1/4 cup liquid.
Heat the olive oil and chili oil in a wok over medium-high heat. Mix in the shrimp, pea pods, and garlic. Cook and stir 2 minutes, until shrimp are almost opaque. Remove from heat, and set aside.
Pour the wine into the wok, and bring to a boil. Cook until reduced by 1/3. Return shrimp, peas, and garlic to the wok, and stir in the reserved pasta water. Continue to cook and stir until shrimp are opaque. Remove wok from heat, and mix in the butter, lemon juice, and basil. Toss with the cooked pasta to serve.
Bring 8 cups of water to boil in a large Dutch oven. Add peas, cook 30 seconds or until crisp-tender. Drain and plunge into ice water; drain. Slice half of peas diagonally.
Combine lemon rind and remaining ingredients in a medium bowl; stir with a whisk. Add peas; toss to coat.