Preheat the oven: Set to 400°F (200°C). If you have an oven-safe skillet (10–12 inches), use it to keep things simple.
Sauté the aromatics: In your skillet or a large pot, heat butter and olive oil over medium heat. Add onion, carrots, and celery.
Cook for 6–8 minutes, stirring occasionally, until softened and lightly golden.
Build flavor: Stir in garlic and thyme. Cook 30–60 seconds until fragrant. Sprinkle in the flour and stir to coat the vegetables.
Cook 1–2 minutes to remove the raw flour taste.
Make the sauce: Gradually whisk in chicken broth, then milk. Keep stirring until smooth. Simmer 3–4 minutes, until slightly thickened and glossy.
Add the good stuff: Stir in chicken, peas, corn, parsley, salt, pepper, and optional soy sauce or Worcestershire.
Taste and adjust seasoning. If not using an oven-safe pan, transfer the filling to a 9x13-inch baking dish.
Mix the biscuit dough: In a bowl, whisk flour, baking powder, baking soda, and salt. Cut in the cold butter with a pastry cutter or fingertips until pea-sized crumbs form.
Stir in chives.
Add buttermilk: Pour in buttermilk and gently mix just until the dough comes together. If dry, add 1–2 tablespoons more buttermilk. Do not overmix—keep it shaggy for tender biscuits.
Top the filling: Scoop the dough in 8–10 mounds over the filling.
Leave a little space between mounds to allow steam to escape. Brush with egg wash if you want extra shine and color.
Bake: Place on the middle rack and bake 20–25 minutes, until the biscuits are puffed and golden and the filling is bubbling around the edges.
Rest and serve: Let the pot pie sit for 10 minutes to set. Scoop into bowls and garnish with more parsley or chives.