Evenly season chicken with 1/4 teaspoon salt and 1/8 teaspoon black pepper. Place the chicken pieces, onion, carrots, coleslaw mix, white beans, stewed tomatoes, peas, chicken broth, 1/2 teaspoon fresh thyme, and bay leaf in the slow cooker and stir. Cover and cook until chicken is fully cooked, on high for 3 to 4 hours or on low for 7 to 8 hours.
Remove and discard the bay leaf. Remove the chicken pieces and place them in a bowl. Shred each piece using 2 forks: one to hold the chicken in place and the other to scrape across the meat and shred it. Return the shredded chicken to the slow cooker, and stir into the soup.
Season the soup with 1/4 teaspoon salt or to taste. Garnish with additional thyme, if using. Serve up and enjoy!