Heat broiler on high.
Rinse the cutlets and pat dry with paper towels. Pound the cutlets to an even thinness. Place on a broiler pan.
In a small bowl, whisk together the hoisin sauce, soy sauce, 1 teaspoon of the rice vinegar, and the fish sauce (if using). Transfer 2 tablespoons of the glaze to a large bowl and stir in the remaining rice vinegar. Add the cabbage, peppers, scallions, and cilantro and toss. Cover and refrigerate.
Pour about 1 tablespoon of the remaining glaze into a small bowl; set aside as a finishing sauce. Brush the chicken with the glaze that remains. Broil, brushing occasionally, until cooked through, 5 to 8 minutes. Spoon the reserved glaze over the top. Serve with the slaw.