Heat broiler to high. Rinse the cutlets, pat dry with paper towels, and pound to an even thinness. Place in 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 1 tablespoon rice vinegar.
Add the cabbage, bell peppers, scallions, and cilantro and toss. Cover and refrigerate.
Pour about 1 tablespoon of the remaining glaze into a small bowl and set aside. Brush the chicken with the glaze that remains.
Broil the chicken, brushing occasionally, until cooked through, 5 to 8 minutes. Spoon the reserved glaze over the top. Serve with the slaw.