Place chicken breasts in a large pot and cover with cold water. Bring to a boil over high heat (about 5 minutes), then reduce heat to medium-low and simmer gently for 12–15 minutes. The chicken is done when a meat thermometer inserted into the thickest part reads 165°F. Remove chicken with a slotted spoon and place on a cutting board to cool for 5 minutes. Checkpoint: Chicken should be white throughout with no pink in the center.

While the chicken cools, prepare the dressing. In a small mixing bowl, whisk together 3 tablespoons sesame oil, 3 tablespoons rice vinegar, 2 tablespoons soy sauce, 1 tablespoon Dijon mustard, 1 tablespoon honey, 1 minced garlic clove, 1 teaspoon grated fresh ginger, and 1/4 teaspoon red pepper flakes. Whisk for about 1–2 minutes until well combined and the honey is dissolved. Checkpoint: The dressing should be smooth and unified in color.

In a dry skillet over medium heat, add 1/2 cup slivered almonds. Toast for 3–4 minutes, stirring frequently, until fragrant and lightly golden. Pour onto a plate to cool completely (about 3 minutes). Checkpoint: Almonds should smell nutty and appear light golden brown.

Once the chicken is cool enough to handle (should be warm or room temperature), shred it into bite-sized pieces using two forks or your hands. Discard any bones or tough bits. You should have about 3 cups of shredded chicken. Checkpoint: All chicken pieces should be roughly the size of your thumb.

In a large mixing or salad bowl, combine 6 cups thinly sliced napa cabbage, 2 cups thinly sliced red cabbage, 1 cup shredded carrots, 1 cup shelled edamame, and 1/2 cup sliced green onions. Toss gently with your hands or two spoons to mix evenly (about 1 minute). Checkpoint: All vegetables should be well distributed and mixed together.

Add the shredded chicken to the vegetable mixture. Pour the prepared dressing over everything (about 30 seconds to pour). Using two large spoons or salad tongs, toss the entire salad for 2–3 minutes, lifting from the bottom and turning over the top until every ingredient is coated with dressing. Checkpoint: Every piece of cabbage and vegetable should glisten with dressing.

Divide the salad among 4 serving bowls or plates (about 2 cups per bowl). The salad should sit on the plate in a generous mound. Sprinkle 1–2 tablespoons of toasted almonds on top of each serving (total 1/2 cup), then add about 1 tablespoon sesame seeds per bowl, and finally top with 1/2 tablespoon of crispy chow mein noodles or wonton strips per serving. Checkpoint: The salad should look colorful, crunchy, and appealing with visible layers of toppings.

Serve immediately at room temperature or slightly chilled. If you prefer a chilled salad, refrigerate the assembled salad for up to 30 minutes before eating. Checkpoint: The salad is ready to eat when it looks fresh and all components are combined.