Shred the chicken breast into bite-sized pieces and set aside. Julienne the carrots into thin 2-inch strips, dice the red bell pepper into 1/4-inch pieces, and slice the scallions. Roughly chop the cilantro and set aside separately. Toast the sesame seeds in a dry pan over medium heat for 2-3 minutes, shaking occasionally, until fragrant—this brings out their nutty flavor and gives them better texture.
In a medium bowl, whisk together the yogurt, mayonnaise, chili sauce, sriracha, lime juice, ginger, onion powder, red pepper, and fish sauce. Mix until completely smooth and well combined. Taste the sauce and adjust the heat or tang to your preference—I like to add a touch more sriracha if I want extra kick, but the current balance should give you that signature bang bang flavor.
Add the shredded chicken, julienned carrots, diced red bell pepper, and sliced scallions to the sauce. Gently fold everything together until the chicken and vegetables are evenly coated. Reserve about half of the chopped cilantro to mix in now, saving the rest for garnish. I recommend folding gently rather than stirring vigorously to keep the chicken tender and prevent it from breaking apart.
Transfer the bang bang chicken salad to a serving bowl or divide among plates. Top with the remaining cilantro, any reserved scallions, and the toasted sesame seeds for a final flourish. Arrange crudités and crackers on the side for serving.