01 - Preheat the oven to 400°F and grease a 9x13-inch baking dish.
02 - Melt the butter in a large skillet over medium heat. Sauté onions, carrots, and celery for 5 minutes until softened, then add garlic and cook for 1 additional minute.
03 - Stir in the flour and cook, stirring constantly, for 1 to 2 minutes to form a roux.
04 - Gradually whisk in chicken broth and whole milk. Bring to a simmer and cook for 3 to 4 minutes until the sauce thickens.
05 - Add shredded chicken, frozen peas, dried thyme, dried sage, salt, and black pepper. Stir to combine, then transfer the filling to the prepared baking dish.
06 - In a large bowl, whisk together flour, baking powder, baking soda, and salt. Cut in cold butter until the mixture resembles coarse crumbs. Stir in buttermilk just until dough forms.
07 - Drop spoonfuls of biscuit dough evenly over the chicken filling, creating 6 to 8 mounds.
08 - Bake for 25 to 30 minutes until biscuits are golden brown and filling is bubbling.
09 - Allow to stand for 5 minutes before serving to set.