01 - Preheat your oven to 400°F (200°C). Grease a 9x13-inch baking dish.
02 - In a large skillet over medium heat, melt 2 tablespoons of unsalted butter. Add the finely chopped yellow onion, diced carrots, and diced celery. Sauté for 5 to 7 minutes until the vegetables begin to soften.
03 - Stir in the minced garlic and cook for an additional 1 minute until fragrant. Sprinkle the all-purpose flour over the sautéed vegetables and cook, stirring constantly, for 2 minutes.
04 - Gradually whisk in the low-sodium chicken broth and whole milk. Bring the mixture to a simmer, stirring occasionally, until it thickens to a sauce consistency, about 5 to 7 minutes.
05 - Stir in the salt, black pepper, dried thyme, dried parsley, frozen peas, and cooked chicken. Allow to simmer for 2 to 3 minutes to meld the flavors. Pour the prepared filling evenly into the greased baking dish.
06 - In a large mixing bowl, whisk together the all-purpose flour, baking powder, baking soda, salt, and sugar. Cut in the cold, diced unsalted butter using a pastry blender or forks until the mixture resembles coarse crumbs.
07 - Pour in the cold buttermilk and gently mix until just combined. Avoid overmixing the dough to ensure tender biscuits.
08 - Drop spoonfuls of the biscuit dough evenly over the chicken filling in the baking dish. For a richer color and shine, optionally brush the tops of the biscuits with a beaten egg.
09 - Bake for 30 to 35 minutes, or until the biscuit topping is golden brown and the filling is bubbling hot.
10 - Allow the casserole to rest for 10 minutes before serving to allow the flavors to settle.