01 - Preheat oven to 400°F and grease a 9x13-inch baking dish.
02 - In a large skillet over medium heat, melt butter. Sauté onions, carrots, and celery for 5 minutes until softened. Add garlic and cook for 1 more minute.
03 - Stir in flour and cook for 1 to 2 minutes, stirring constantly to form a roux.
04 - Gradually whisk in chicken broth and milk. Simmer for 3 to 4 minutes until the sauce thickens.
05 - Incorporate shredded chicken, peas, thyme, sage, salt, and pepper into the sauce. Mix thoroughly and transfer to the prepared baking dish.
06 - Whisk together flour, baking powder, baking soda, and salt in a large bowl. Cut in cold butter until mixture resembles coarse crumbs. Stir in buttermilk until just combined into a dough.
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 and filling is bubbly.
09 - Allow casserole to rest for 5 minutes before serving.