Preheat the oven to 375°F, positioning the rack in the center.
In a large skillet set over medium-high heat, melt the butter. Add the carrots, celery, onion, thyme, and ½ teaspoon of the salt, cooking and stirring frequently until the vegetables are softened, approximately 5 to 7 minutes.
Stir in the flour to coat the vegetables and continue cooking for an additional 2 minutes.
Pour in the milk, chicken broth, Dijon mustard, garlic powder, and remaining ½ teaspoon salt, whisking thoroughly to blend. Raise the heat to high and bring the mixture to a boil.
Reduce to medium heat and simmer, stirring regularly, until the sauce thickens, about 3 to 5 minutes. Incorporate the shredded chicken and peas, tasting and adjusting the seasoning as necessary.
Spoon the prepared filling into a 13-by-9-inch baking dish. Evenly place the biscuits over the surface of the filling. Lightly season the top with additional salt and pepper.
Bake for 22 to 25 minutes, or until the filling is bubbling and the biscuits are puffed and golden brown. Allow the dish to rest for 5 minutes before serving.