In a large skillet, heat olive oil over medium heat. Add the diced onions and celery, and sauté until softened, about 5-7 minutes.
Stir in the frozen peas and carrots, cooking for an additional 3 minutes.
In a separate bowl, whisk together the flour, garlic powder, onion powder, thyme, salt, and black pepper.
Gradually add the chicken broth and milk to the flour mixture, whisking continuously to prevent lumps.
Pour the broth mixture into the skillet with the sautéed vegetables and bring to a simmer, stirring constantly until the mixture thickens slightly, about 5 minutes.
Add the shredded chicken to the skillet, mixing well to combine. Remove from heat and transfer the filling into a greased 9-inch pie dish.
Bake the crustless pie in the preheated oven for 30-35 minutes, or until bubbly and golden on top.
Remove from the oven and allow to cool for a few minutes before serving.
Garnish with chopped fresh parsley before slicing to serve.