In a glass bowl mix together first six ingredients with a fork or small whisk and add chicken breast. Marinate for 30 minutes or longer.
Spray crock of slow cooker with nonstick cooking spray. Turn slow cooker to high.
Add chicken breast to bottom of slow cooker and cover. Turn chicken every 15 minutes until browned on all sides.
Turn slow cooker to low. Add frozen vegetables on top of browned chicken. Break dry noodles in half and add on top of frozen vegetables. Top with cabbage and carrots.
Mix chicken broth, soy sauce, Hoisin, garlic powder, brown sugar, sesame oil, and rice wine vinegar together in a bowl with a fork or small whisk. Pour over the cabbage / carrot mixture.
Place lid on slow cooker and cook for four hours on low.
After two hours, remove lid and toss ingredients lightly, to make sure the noodles are separated and immersed in the liquid.
Return lid and continue to cook until noodles are done.