Preheat the oven to 400°F (200°C).
In a large skillet, heat olive oil over medium heat. Add the chopped onion, carrots, and celery. Cook for 5-7 minutes until vegetables are tender.
Add the minced garlic and cook for 1 minute until fragrant.
Sprinkle the whole wheat flour over the vegetables and stir well to coat. Cook for 2 minutes, stirring constantly.
Gradually pour in the low sodium chicken broth while stirring to avoid lumps.
Add the unsweetened almond milk, dried thyme, dried rosemary, salt, and black pepper. Stir and cook until the mixture thickens, about 3-5 minutes.
Add the shredded chicken and frozen peas to the skillet. Stir to combine and heat through for 2 minutes. Remove from heat.
Transfer the chicken and vegetable mixture into a 9-inch pie dish.
Unroll the whole wheat pie crust and place it over the filling. Trim any excess crust and press the edges to seal. Cut a few small slits in the crust to allow steam to escape.
Bake in the preheated oven for 25-30 minutes, or until the crust is golden brown.
Remove from the oven and let it cool for 5 minutes before serving.
Garnish with chopped fresh parsley and serve warm.