Raspberries add tangy sweetness to these pita sandwiches.
In a medium saucepan, combine 4 cups water, 2 teaspoons salt, the peppercorns, sliced shallots, and chicken; bring to a simmer over medium-low heat, and continue cooking until the chicken is cooked through, about 12 minutes. Transfer the chicken to a plate; let cool completely, and cut into 1/2-inch dice.
Make the vinaigrette: In a small bowl, whisk together the vinegar, remaining 1/2 teaspoon salt, sugar, minced shallot, and cardamom. Slowly whisk in the oil until mixture is emulsified.
In a medium bowl, combine chicken, fennel, and walnuts. Pour vinaigrette over; toss to coat. Season with salt and pepper. Gently fold in raspberries.
Slice off 1 inch from one side of each pita; gently open. Fill with a handful of mache; spoon in chicken mixture. Serve.