Season the chicken pieces with salt and freshly ground black pepper.
In a small bowl, whisk together the chicken broth, soy sauce, grated ginger, hoisin sauce, rice vinegar, and cornstarch until smooth.
Heat the sesame oil in a large skillet over medium heat.
Add the seasoned chicken to the hot skillet and cook, stirring or flipping once, until cooked through, about 5 minutes depending on piece size.
Add the minced garlic to the skillet and cook for about 30 seconds until fragrant.
Reduce heat to low and pour the sauce mixture into the skillet. Stir continuously until the sauce thickens and coats the chicken, about 1–2 minutes.
Stir in Sriracha to taste, then add the cashews and most of the chopped green onions, reserving some for garnish.
Spoon the chicken and cashew mixture into lettuce leaves, top with the remaining green onions, and serve immediately.