Preheat the oven to 375°F (190°C).
Heat the olive oil in a large skillet over medium heat.
Add the chopped onion, diced carrots, and diced celery to the skillet. Cook for 5-7 minutes, stirring occasionally, until the vegetables are softened.
Add the minced garlic and cook for 1 minute until fragrant.
Add the chicken breast pieces to the skillet and cook until they are no longer pink, about 5 minutes.
Sprinkle the whole wheat flour over the chicken and vegetables. Stir well to coat and cook for 2 minutes to remove the raw flour taste.
Slowly pour in the chicken broth while stirring continuously to avoid lumps.
Add the skim milk, dried thyme, dried parsley, black pepper, and salt. Stir to combine.
Bring the mixture to a simmer and cook for 5-7 minutes until the sauce thickens.
Stir in the thawed peas and remove the skillet from heat.
Transfer the chicken and vegetable filling into a 9-inch pie dish.
Place the whole wheat pie crust over the filling, trimming any excess dough and pressing the edges to seal.
Brush the beaten egg white over the crust to give it a light golden color when baked.
Cut a few small slits in the crust to allow steam to escape.
Bake the pie in the preheated oven for 25-30 minutes or until the crust is golden brown and the filling is bubbling.
Remove from the oven and let the pie cool for 5 minutes before serving.