Make the teriyaki sauce: In a liquid measuring cup or medium bowl, combine the brown sugar, soy sauce, lemon juice, sesame seeds, ginger, and garlic. Whisk to combine and dissolve the sugar.
Butterfly the chicken breasts, then place in a high-walled baking dish. Pour the teriyaki sauce over the chicken, reserving ½ cup (120 ml) of the sauce. Cover the dish with plastic wrap and marinate the chicken in the refrigerator for 20 minutes.
Preheat the oven to 375˚F (190˚C). Line a baking sheet with foil.
Make the dressing: While whisking, slowly drizzle the olive oil into the reserved teriyaki sauce.
Transfer the marinated chicken breasts to the prepared baking sheet. Bake for 25-30 minutes, or until the internal temperature reaches 160˚F (70˚C). Let cool for 10 minutes.
In a medium bowl, use 2 forks to shred the chicken. Pour ¼ cup (60 ml) dressing over the chicken and toss to coat.
Prepare the salad: Add the lettuce to a large bowl. Top with the mango, bell peppers, green beans, avocado, and shredded chicken. Add the remaining dressing and toss well.
Divide between serving bowls and top with the scallions.