01 - In a large slow cooker, place chicken, onion, carrots, celery, garlic, chicken broth, dried thyme, dried parsley, black pepper, salt, and unsalted butter.
02 - Cover and cook on LOW for 4 hours or on HIGH for 2 hours until the chicken is tender.
03 - Remove chicken, shred it using two forks, then return the shredded chicken to the slow cooker.
04 - Whisk heavy cream and 1/4 cup flour in a small bowl until smooth, then stir into the slow cooker to thicken the broth.
05 - Stir in frozen peas, chopped green beans, and corn kernels until evenly combined.
06 - In a medium bowl, whisk flour, baking powder, and salt. Cut in cold butter until mixture resembles coarse crumbs. Stir in milk and parsley to form a soft dough.
07 - Drop spoonfuls of dumpling dough (approx. 1 tablespoon each) 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.