Heat oil in a Dutch oven (I use avocado oil because it has a high smoke point) over medium high heat. Pat the chicken dry with a paper towel and season with salt and pepper.
Working in batches so you don’t overcrowd the pan, sear the chicken until golden brown, about 3 minutes per side. Remove chicken and set aside, pour excess fat from pan.
Add butter to the Dutch oven and then the carrots, celery and onion with a pinch of salt. Sauté until soft, 5-10 minutes .
Add the flour to the pan and stir together until combined and no dry spots remain.Whisk in wine, stirring and scraping brown bits from the bottom of the pan.
Add the chicken broth, milk, thyme and bay leaves. Return the chicken to the pot, stir to cover the chicken with liquid. Reduce heat to low, cover, and simmer until chicken is fully cooked and tender, about 30 minutes.
When chicken is cooked and tender, remove from pan and shred with two forks, then return meat to pot. Next, make the dumplings.
Make the dumplings and finish stew
Whisk together the flour, baking powder and salt in a small bowl, set aside.
Warm the milk and butter in a microwave safe container until butter is melted.
Pour the warm milk and butter mixture into the flour mixture and gently stir to combine, just until no dry spots of flour remain. Don’t over mix.
Add the peas and parsley to the stew, taste stew and add salt and pepper if needed.
Using a medium cookie scoop, or two spoons, scoop batter into balls about two tablespoons each, and drop into the chicken stew. Be sure stew is gently simmering and not boiling.
Cover and simmer until dumplings are cooked through, about 15 minutes.