1. In a large saucepan, bring 8 cups water to a gentle simmer. Generously salt water. Add thyme, rosemary, bay leaves, and pepper. Add chicken and simmer until chicken registers 160 degrees on an instant-read thermometer. Remove from heat and let chicken cool in liquid. Store chicken in liquid, covered and refrigerated, until ready to use.

2. Preheat a sandwich press according to the manufacturer's instructions.

3. Remove chicken breast from poaching liquid and thinly slice; divide evenly among 4 slices of bread. Spread pesto on top of chicken; top with peppers and mozzarella. Sandwich with remaining 4 slices of bread and place on sandwich press. Close the lid and apply slight pressure; cook until bread is golden and cheese is melted, 5 to 8 minutes. If bread is sticking to the press, continue to cook and bread will unstick itself. If press is generating more heat from the bottom, flip the sandwich halfway through cooking.

4. Remove sandwich from press and cut in half before serving.