01 - Preheat your oven to 400°F. In a large skillet or Dutch oven, melt the butter over medium heat. Add diced onion, carrots, and celery; sauté for 5–6 minutes until softened. Stir in minced garlic and cook for 1 additional minute.
02 - Sprinkle the all-purpose flour over the sautéed vegetables and stir constantly for 1–2 minutes until the flour is lightly golden. Gradually whisk in the chicken broth and whole milk. Bring the mixture to a simmer, stirring frequently, until it has thickened, approximately 3–4 minutes.
03 - Add the cooked chicken, frozen peas, fresh thyme, salt, and black pepper to the thickened sauce. Stir to thoroughly combine all ingredients, then remove the skillet from the heat.
04 - Pour the prepared chicken filling evenly into a 9x13-inch baking dish or a similar ovenproof dish.
05 - In a large mixing bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt for the biscuit topping.
06 - Add the cold, diced butter to the dry ingredients. Using a pastry cutter or your fingertips, cut the butter into the flour mixture until it resembles coarse crumbs.
07 - Stir in the cold buttermilk and chopped fresh parsley (if using) just until the dough comes together. Be careful not to overmix the dough.
08 - Drop 6–8 spoonfuls of the biscuit dough evenly over the chicken filling in the baking dish.
09 - Bake for 25–30 minutes, or until the biscuit topping is golden brown and the chicken filling is bubbling hot.
10 - Allow the chicken pot pie to rest for 10 minutes after baking before portioning and serving.