Place the chicken in a bowl with a tight fitting lid or sturdy resealable bag. Add soy sauce, hoisin sauce, sesame oil, and pepper, then seal and squish to coat the chicken. Place in the fridge for at least 30 minutes to marinate.
Preheat oven to 350 degrees F. Place the chicken in a baking dish, then bake for 15 to 20 minutes until the chicken reaches 165 degrees F when tested with an instant read digital meat thermometer.
Remove the chicken to a cutting board to rest for 5 minutes before cutting into strips.
Break up the hard ramen noodles and scatter onto a baking sheet. Add the almonds and sesame seeds.
Bake noodles for 8 minutes until toasted, then set aside to cool.
Assemble the salad in a large bowl by combining the cabbage, grated carrot, sugar snap peas, edamame, and green onions. Toss to evenly distribute.
Add the sliced chicken, toasted ramen and almonds, cilantro, and mandarin oranges on top.
Combine dressing ingredients in a jar with a tight lid and shake well to combine. Drizzle over the salad just before serving.