In a large skillet over medium heat, melt the butter. Add the onion, carrots, and celery, cooking until softened, about 5 minutes.
Sprinkle the flour over the sautéed vegetables, stirring well to combine, and cook for another 2 minutes.
Gradually whisk in the chicken broth and milk, ensuring there are no lumps. Continue to stir until the mixture thickens, about 3-4 minutes.
Add the shredded chicken, diced potatoes, peas, garlic powder, thyme, salt, and pepper to the skillet. Stir until well combined and heated through, then remove from heat.
Pour the mixture into a greased 9-inch pie dish or oven-safe baking dish.
Place the dish in the preheated oven and bake for 25-30 minutes, until the top is golden and bubbly.
Remove from the oven and let it cool slightly before garnishing with fresh parsley. Serve warm.
Notes
Feel free to add other vegetables like corn or green beans.