01 - Preheat oven to 400°F.
02 - In a large skillet over medium heat, melt the butter. Add onion, carrots, and celery. Sauté for 5–6 minutes until softened.
03 - Add garlic and cook for 1 minute. Stir in the flour and cook, stirring constantly, for another minute to create a roux.
04 - Gradually stir in chicken broth and milk. Bring to a simmer and cook until thickened, about 5–7 minutes.
05 - Add the diced chicken, peas, salt, pepper, thyme, and parsley. Stir to combine. Remove from heat.
06 - Pour the filling into a 9x13-inch baking dish or deep pie dish.
07 - In a bowl, combine flour, baking powder, baking soda, and salt for the biscuit crust. Cut in the cold butter with a pastry cutter or fingers until the mixture resembles coarse crumbs.
08 - Stir in the buttermilk just until the dough comes together. Do not overmix.
09 - Drop spoonfuls of biscuit dough evenly over the filling, or gently pat the dough and lay over the top.
10 - Bake for 25–30 minutes, or until the biscuit crust is golden brown and the filling is bubbling.
11 - Let stand for 10 minutes before serving to allow the filling to set.