In a mixing bowl, combine the peanut butter, soy sauce, honey, sesame oil, minced garlic, grated ginger, and chicken broth. Mix until smooth to create the peanut sauce.
Place the boneless chicken breasts at the bottom of the slow cooker. Pour the peanut sauce mixture over the chicken, making sure it is well coated.
Cover the slow cooker and cook on low for 6 hours, or until the chicken is tender and easily shredded with a fork.
About 30 minutes before serving, cook the rice noodles according to package instructions. Drain and set aside.
Once the chicken is cooked, shred it in the slow cooker using two forks and stir to mix it with the sauce.
Add the rice noodles and shredded carrots to the slow cooker, mixing well to combine everything.
Let it sit for an additional 10 minutes on the low setting to warm everything through.
Serve the chicken peanut noodles garnished with chopped green onions and chopped peanuts.