Cook the chicken in the chicken broth until fully cooked.
Remove the chicken and shred it into bite-sized pieces; set aside.
Sauté onion, carrots, and celery in the same pot until softened.
Return the shredded chicken back into the pot, along with the chicken broth, peas, and thyme.
Prepare the biscuit dough by mixing flour, baking powder, and salt.
Cut in the butter, then stir in the milk until just combined.
Drop spoonfuls of the biscuit dough into the simmering broth.
Cover and simmer until the dumplings are cooked through, about 15 minutes.
Serve warm, garnished with fresh herbs if desired.