Set your oven to 375º and place a rack in the middle.
In a large skillet, melt the butter over medium-high heat. Add the diced carrots, celery, onion, thyme, and half of the salt. Sauté, stirring regularly, until the vegetables soften, about 5 to 7 minutes.
Sprinkle the flour over the veggies and stir well to coat. Let this cook for another 2 minutes to remove the raw flour taste.
Pour in the milk, chicken broth, Dijon mustard, garlic powder, and the rest of the salt. Whisk everything together and bring the mixture to a boil over high heat. When it starts boiling, lower the heat to medium and let it gently simmer, stirring often, until the sauce thickens, which should take between 3 and 5 minutes.
Fold in the cooked shredded chicken and frozen peas, then taste and add extra salt if needed.
Transfer the filling to a 13-by-9-inch baking dish. Place the biscuit dough pieces evenly on top of the filling and sprinkle everything with black pepper and a little salt.
Bake in the preheated oven until the filling bubbles and the biscuits turn golden and have risen nicely, about 22 to 25 minutes.
Allow it to sit for 5 minutes before serving to let it set slightly.