In a saucepan, combine the vinegar, 2 teaspoons of the lemon juice, peppercorns, 1/2 teaspoon salt, and thyme. Add the chicken breasts and enough water to cover by 1 inch. Bring to a boil over high heat. Skim off any scum that rises to the surface with a slotted spoon. Reduce the heat to medium low and simmer for 10 minutes.
Remove from the heat and allow the chicken to cool in the liquid for 45 minutes.
Once the chicken is cool, transfer to a cutting board and coarsely chop. Discard poaching liquid.
Transfer the chicken to a mixing bowl and add the mayonnaise, the remaining 2 teaspoons of lemon juice, celery, parsley, remaining 1/4 teaspoon of salt, and white pepper. Use a wooden spoon to stir until thoroughly combined.
Divide the chicken salad among 4 slices of bread, about 2/3 cup per sandwich. Top with another slice of bread and serve immediately.
YIELD: 4 super-stuffed sandwiches
Options to add to salad:
Chopped fresh dill or tarragon
Sweet pickle relish