01 - Preheat the oven to 400°F.
02 - In a large skillet or saucepan, melt butter over medium heat. Add onion, carrots, and celery; sauté for 5 to 6 minutes until softened.
03 - Stir in minced garlic and cook for 1 minute.
04 - Sprinkle flour over vegetables and cook, stirring constantly, for 1 to 2 minutes.
05 - Gradually whisk in chicken broth and milk, avoiding lumps. Bring to a simmer and cook until thickened, about 3 to 4 minutes.
06 - Stir in cooked chicken, peas, salt, pepper, thyme, and parsley. Simmer for 2 to 3 minutes, then remove from heat.
07 - Pour the filling into a 9x13-inch baking dish or large oven-safe skillet.
08 - In a large bowl, whisk together flour, baking powder, baking soda, and salt. Cut in cold butter with a pastry cutter or fingers until mixture resembles coarse crumbs.
09 - Pour in cold buttermilk and stir until just combined; avoid overmixing.
10 - Drop heaping spoonfuls of biscuit dough evenly over the filling, spreading slightly but leaving gaps for steam.
11 - Lightly brush biscuit tops with additional buttermilk.
12 - Bake uncovered for 25 to 30 minutes until biscuits are golden brown and filling is bubbling.
13 - Allow to cool for 5 minutes before serving.