01 - Set the oven to 400°F and allow it to reach temperature.
02 - Melt butter in a large skillet over medium heat. Add diced onion, carrots, and celery; cook for 5 to 6 minutes until softened.
03 - Stir in minced garlic and cook for an additional minute to release aroma.
04 - Sprinkle flour over the vegetables and stir continuously for 1 to 2 minutes to eliminate raw flour taste.
05 - Gradually whisk in chicken broth and whole milk, preventing lumps. Bring mixture to a simmer and cook until thickened, about 3 to 4 minutes.
06 - Mix in cooked chicken, peas, salt, pepper, thyme, and parsley. Stir well and simmer for 2 to 3 minutes. Remove from heat.
07 - Transfer the filling evenly into a 9x13-inch baking dish or a large oven-safe skillet.
08 - In a large bowl, whisk together flour, baking powder, baking soda, and salt. Cut in cold butter until mixture resembles coarse crumbs.
09 - Pour cold buttermilk into the dry ingredients and stir gently until just combined, avoiding overmixing.
10 - Drop heaping spoonfuls of biscuit dough evenly over the hot filling, spreading slightly while leaving small gaps for steam to escape.
11 - Lightly brush the tops of the biscuits with additional buttermilk for a golden finish.
12 - Place dish in the oven and bake for 25 to 30 minutes until biscuits are golden brown and filling is bubbling.
13 - Allow to rest for 5 minutes to set before serving.