01 - Preheat oven to 400°F (200°C).
02 - In a large skillet or Dutch oven, melt butter over medium heat. Add diced onion, carrots, and celery; sauté until vegetables are tender, about 5 minutes.
03 - Incorporate minced garlic and cook for 1 minute. Sprinkle flour over the vegetables and stir thoroughly, cooking for 1–2 minutes to eliminate raw taste.
04 - Gradually whisk in chicken broth and whole milk. Cook, stirring frequently, until the sauce thickens, approximately 5 minutes.
05 - Stir in cooked chicken, frozen peas, dried thyme, salt, black pepper, and fresh parsley if using. Mix well and simmer for 2 minutes. Remove from heat.
06 - Pour the prepared filling into a 9x13-inch baking dish or similar casserole dish.
07 - In a large mixing bowl, whisk together flour, baking powder, baking soda, and salt. Add cold butter and use a pastry cutter or fork to blend until mixture forms coarse crumbs.
08 - Pour in cold buttermilk and gently mix just until dough forms. Handle minimally and avoid overmixing.
09 - Drop generous spoonfuls of biscuit dough evenly over filling in the dish, covering most of the surface. Lightly brush tops with additional buttermilk.
10 - Bake for 30–35 minutes until biscuits are golden brown and filling is bubbling. Allow to rest for 5 minutes before portioning and serving.