Spread the diced onion over the bottom of a slow cooker.
Arrange the chicken thighs over the onion in a single layer.
In a medium bowl, stir together the cream of chicken soup, cream of celery soup, poultry seasoning, chopped parsley, and black pepper.
Spoon the soup mixture over the chicken and spread it roughly across the top.
Pour the chicken broth into the slow cooker.
Cover and cook on HIGH for about 5 hours.
Leave the lid closed during the first 4 hours so the slow cooker can maintain its temperature.
When about 1 hour of cooking time remains, add the thawed mixed vegetables.
Shred the tender chicken directly in the crockpot using two forks or a sturdy spoon. Stir the chicken and vegetables into the creamy broth.
Remove the biscuits from the can and flatten each one slightly.
Cut each biscuit into about four strips or several smaller dumpling-size pieces.
Scatter the biscuit pieces evenly over the chicken mixture.
Gently press the dough down until the bottoms touch the hot broth, but avoid completely submerging every piece.
Cover again and continue cooking on HIGH for about 1 hour, or until the biscuit dumplings are puffed and cooked through.
Tear open one of the thickest dumplings before serving. If the center still looks wet or doughy, continue cooking until done.
Give the chicken and dumplings a gentle stir and serve hot.