Prepare Chicken: Rub chicken pieces with salt, pepper, and poultry seasoning. Place breasts in a 6-qt. slow cooker; top with thighs. Add carrots and next 3 ingredients. Whisk together soup and broth until smooth. Pour soup mixture over vegetables. Cover and cook on HIGH 3 1/2 hours or until chicken shreds easily with a fork. Remove chicken; cool 10 minutes. Bone and shred chicken. Stir chicken into soup-and-vegetable mixture. Cover and cook on HIGH 1 hour or until boiling.
Meanwhile, prepare Dumplings: Whisk together flour and next 3 ingredients. Make a well in center of mixture. Add milk, butter, thyme, and parsley to dry ingredients, gently stirring just until moistened.
Drop dough by 1/4 cupfuls into simmering chicken mixture, leaving about 1/4-inch space between dumplings. Cover and cook on HIGH 30 to 35 minutes or until dumplings have doubled in size.