Here's a lighter, sexier chicken salad for summer with a tropical twist. This is fantastic served on some flatbread crisps, some toasted buns, plain old sandwich bread, or in lettuce cups.
Set the chicken on a plate and season with ½ teaspoon of the salt. Set aside for 20 minutes at room temperature.
Meanwhile, in a medium-sized saucepan, combine the olive oil, shallot, and garlic and cook over medium heat, stirring often, until the shallot is translucent, 4-5 minutes. Stir in the thyme sprigs, bay leaves, and remaining salt, then pour in the chicken broth and the water.
Juice the lemon and add the juiced lemon halves to the saucepan. Bring the broth to a simmer, then add the chicken breasts and reduce the heat to low. Gently cook the chicken in the broth until it registers 160 degrees on an instant-read thermometer, about 30 minutes.
Line a plate with paper towels. Turn off the heat and let the chicken cool in the broth for 10 minutes, then remove the chicken breasts from the broth and set on the paper towels to cool. When the chicken breasts are cool enough to handle, use 2 forks to shred them.
Preheat the oven to 350 degrees.
Place the pistachios on a rimmed baking sheet and bake until fragrant and toasted, 5-6 minutes. Remove from the oven and transfer the pistachios to a cutting board. Once cool, roughly chop and set aside. (If serving the chicken salad on buns, place the buns on a baking sheet and toast them in the oven.)
In a large bowl, whisk together the lemon juice, mustard, tarragon, and salt. While whisking, slowly drizzle in the olive oil until all of the olive oil is added and the vinaigrette is thick and creamy. Add the pulled chicken to the bowl along with the pistachios, mango, celery, and scallions. Gently toss to coat and serve on flatbread crisps or buns, or wrapped in lettuce leaves.