Prepare the crispy rice according to your preferred method. Cook until golden and crisp, then set it aside while you assemble the remaining ingredients.
Add the Greek yogurt, mayonnaise, rice vinegar, 1 teaspoon sriracha, honey, and salt to a medium bowl. Whisk until completely smooth and creamy.
Taste the dressing. Add the remaining sriracha for extra heat or a small pinch of salt if needed.
Divide the chopped mixed greens evenly between four serving bowls.
Arrange the shredded chicken, cucumber, grated carrot, cilantro, pickled red onion, and crispy rice over the greens.
Generously drizzle the dressing over each Bang Bang Chicken Salad just before serving.
Finish with additional cilantro if desired and serve immediately while the rice is still crunchy.