Place chicken, onion, carrots, celery, garlic, thyme, salt, pepper, and chicken broth into the Instant Pot.
Seal the lid and set to high pressure for 12 minutes. Allow natural release for 10 minutes. Remove the chicken and shred with two forks.
In a bowl, combine flour, baking powder, salt, milk, and melted butter to form soft dough. It is okay if it is a little sticky.
Pour milk into the Instant Pot, stir in shredded chicken and frozen peas.
Drop spoonfuls of dumpling dough into the soup. Close lid and set Instant Pot to Steam for 5 minutes. Quick release when done.
Spoon soup into bowls. Optional: sprinkle with fresh parsley.