Preheat your oven to 375°F (190°C) and lightly grease a 9x13 inch baking dish.
In a medium saucepan, melt 4 tablespoons butter over medium heat. Add the diced onion, celery, and carrots. Sauté until vegetables begin to soften, about 5-7 minutes.
Sprinkle the flour over the vegetables and stir constantly for 1-2 minutes to cook the flour.
Gradually whisk in the chicken broth and milk, stirring continuously to prevent lumps from forming.
Bring the mixture to a simmer and cook until thickened, about 3-5 minutes. The sauce should coat the back of a spoon.
Add the thyme, sage, garlic powder, salt, and pepper. Stir to combine.
Fold in the cooked chicken, frozen peas, and fresh parsley. Remove from heat and pour the mixture into the prepared baking dish.
For the biscuit topping, combine flour, baking powder, and salt in a large mixing bowl.
Cut in the cold cubed butter using a pastry cutter or your fingertips until the mixture resembles coarse crumbs.
Add the cold milk and stir just until a soft dough forms. Do not overmix.
Drop spoonfuls of the biscuit dough evenly over the chicken mixture, using about 8-10 biscuits total.
Optional: Brush the tops of the biscuits with melted butter for extra browning.
Bake in the preheated oven for 30-35 minutes, until the biscuits are golden brown and the filling is bubbling around the edges.
Allow the casserole to rest for 5-10 minutes before serving.