In a large dutch heat oil over medium heat. Once hot, add chicken breasts and brown on each side. About 5-7 minutes per side. Once cooked through, remove to a plate to the side. Once cool, dice into bite sized pieces.
To dutch oven, melt butter over medium heat. Add diced onions, carrots, and celery. Saute until just tender, about 5 minutes. Add salt, pepper, and thyme.
To the pot of cooked veggies with butter, add flour and stir to create a roux. Cook until the flour taste disappears, 1-2 minutes.
Slowly whisk in chicken stock until thickened. Add peas, milk, and cooked diced chicken. Simmer for 10 minutes.
In a medium bowl, combine flour, salt, and baking powder. Add in melted butter and milk until the dough just comes together.
Gently tear off pieces of dough and add to the pot that's simmering. It is ok if the dumplings are touching. Cover and let cook for 15 minutes, flipping the dumplings halfway through. Serve topped with fresh parsley.