In a large skillet, melt the butter over medium heat. Add the chopped onion, diced carrots, and diced celery. Sauté until softened and fragrant, about 5-7 minutes.
Sprinkle the flour over the sautéed vegetables and stir well. Cook for another minute to create a roux.
Gradually pour in the chicken broth and whole milk while whisking continuously. Cook for 3-5 minutes until thickened to a creamy consistency.
Remove from heat and stir in the shredded chicken, frozen peas, garlic powder, dried thyme, salt, and pepper.
Pour the filling into a 9-inch pie dish, spreading it evenly.
Open the biscuit dough and separate the biscuits. Lay them on top of the chicken mixture, slightly overlapping.
Bake for 20-25 minutes until the biscuits are golden brown.
Allow to cool for a few minutes before serving.
Notes
Serve garnished with fresh parsley for added color.