1. Poach the chicken: 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 saucepan set over medium heat, add the olive oil, shallot and garlic and cook, stirring often, until the shallot is translucent, 4 to 5 minutes. Stir in the thyme sprigs, bay leaves and remaining 2 teaspoons of salt, then pour in the chicken broth and water.

2. Juice the lemon and set the lemon juice aside for the vinaigrette. 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° on an instant-read thermometer, about 30 minutes. Turn off the heat and cool the chicken in the broth for 10 minutes, then remove the chicken breasts from the broth and set on a paper-towel-lined plate to cool for 10 minutes. When the chicken breasts are cool enough to handle, use two forks to shred them into shards. Set aside.

3. Make the salad: Preheat the oven to 350°. On a rimmed baking sheet, place the walnuts and bake them until fragrant and toasted, 5 to 6 minutes. Remove from the oven and transfer the walnuts 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.)

4. In a large bowl, whisk together the lemon juice, mustard, tarragon and salt together. 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 walnuts, grapes, celery and scallions. Gently toss to coat and serve on flatbread crisps, buns or wrapped in lettuce leaves.