01 - Preheat oven to 400°F.
02 - Melt butter in a large skillet over medium heat. Add onion, carrots, and celery. Sauté for 5–6 minutes until softened.
03 - Stir in minced garlic and cook for 1 minute until fragrant.
04 - Sprinkle flour over vegetables and stir to coat. Cook for 1–2 minutes, stirring constantly.
05 - Gradually pour in chicken broth and milk, whisking to avoid lumps. Bring to a simmer and cook until thickened, 4–5 minutes.
06 - Add cooked chicken, peas, thyme, salt, and pepper. Simmer for 2 minutes. Taste and adjust seasoning as needed. Remove from heat.
07 - Pour filling into a 9x13-inch baking dish or large deep pie dish.
08 - In a large bowl, whisk together flour, baking powder, salt, and baking soda.
09 - Cut in cold butter using a pastry cutter or fingers until mixture resembles coarse crumbs.
10 - Add cold buttermilk and stir just until dough comes together. Do not overmix.
11 - Drop large spoonfuls of biscuit dough evenly over the filling. Gently spread to cover most of the surface. Brush with extra buttermilk for a golden finish.
12 - Bake for 25–30 minutes, or until biscuits are golden and filling is bubbling.
13 - Let cool for 10 minutes before serving.