01 - Add chicken, onion, carrots, celery, garlic, chicken broth, dried thyme, dried parsley, black pepper, salt, and butter to a large slow cooker.
02 - Cover and cook on LOW for 4 hours or on HIGH for 2 hours until the chicken is tender.
03 - Remove chicken from slow cooker, shred using two forks, then return shredded chicken to the slow cooker.
04 - Whisk heavy cream and 1/4 cup flour together until smooth, then stir into the slow cooker to thicken the broth.
05 - Stir in peas, green beans, and corn kernels until evenly combined.
06 - In a medium bowl, whisk all-purpose flour, baking powder, and salt. Cut in cold butter with a fork or pastry cutter until the mixture resembles coarse crumbs. Stir in milk and parsley to form a soft dough.
07 - Drop spoonfuls (approximately 1 tablespoon each) of dumpling dough onto the surface of the stew in the slow cooker.
08 - Cover and cook on HIGH for 1 hour until dumplings are puffed and cooked through.
09 - Taste and adjust seasoning if necessary. Serve hot.