Place chicken breasts in a single layer in a medium saucepan. Add chicken broth, bay leaf, thyme sprigs, and peppercorns. Bring to a gentle simmer over medium heat, then reduce heat to low, cover, and cook until chicken is cooked through and reaches an internal temperature of 165°F, about 15-20 minutes.
Remove chicken from broth and let cool slightly. Shred or slice thinly. Discard poaching liquid and aromatics.
In a small bowl, combine mayonnaise, yogurt, lemon juice, dill, chives, salt, and pepper. Mix well.
Spread the herb mayo mixture evenly on 4 slices of toasted bread.
Divide the shredded chicken among the 4 mayo-spread slices. Top with arugula, cucumber slices, and red onion slices. Season with a pinch of salt and pepper.
Close sandwiches with remaining bread slices. Cut in half and serve immediately.
Tips
For extra flavor, add a pinch of smoked paprika or cayenne to the herb mayo.
The poached chicken can be made ahead and refrigerated for up to 3 days.
If not serving immediately, wrap sandwiches tightly in plastic wrap and refrigerate for up to 4 hours.