Heat oil in a heavy bottomed large pot on high until smoking.
Sear the chicken thighs until golden brown on both sides, remove from pan and set aside. If there is a lot of excess grease at this point, remove it from the pan.
Reduce heat to medium low and add butter to the pot.
Once the butter is melted, add the carrots, celery, and onion. Saute until slightly softened.
Add thyme, sage, salt, pepper, and garlic and cook until fragrant, about 30 seconds.
Add flour and stir until all the vegetables are coated. Cook for about 2 minutes.
Add white wine, stirring constantly and scraping up any browned bits on the bottom of the pan.
Add chicken broth, milk, and cream. Stir to combine.
Add chicken and any accumulated juices back into the pot, nestling it down in the vegetables.
Cover and simmer about 45 minutes, until chicken is cooked through and shreds easily.
Remove chicken, shred, and add back to the pot.
Stir in the frozen peas and return stew to a simmer.
For the Dumplings
Whisk dry ingredients together.
Stir in milk and butter until a soft dough forms.
After the stew has been brought back up to a simmer once you have added the peas, drop rounded spoonfuls of the dough into the stew. They should be about the size of a golf-ball, the dough should make about 9 dumplings.
Space them evenly in the stew.
Cover the pot and simmer 15-18 minutes, or until the dumplings are cooked through.
Sprinkle with chopped parsley.
Boneless, skinless chicken breasts can be used but are often more dry and take longer to cook.Bone-in, skin-on chicken breasts can also be used but will also take longer to cook.Chicken broth can always be substituted in place of white wine.