Cook the chicken: Place chicken breasts in a pot, cover with salted water, bring to a boil, then reduce to a simmer. Cook for 12-15 minutes until internal temp reaches 165°F. Let cool slightly, then shred with two forks. (Or use leftover rotisserie chicken.)
Make the dressing: In a small bowl, whisk together mayonnaise, sour cream, apple cider vinegar, Dijon mustard, honey, salt, and pepper until smooth. Taste and adjust seasoning.
Combine: In a large bowl, toss together shredded chicken, cabbage, carrots, and green onions. Pour dressing over and mix well.
Chill: Cover and refrigerate for at least 30 minutes to let flavors meld. Before serving, stir in toasted almonds if using. Serve cold or at room temperature.