Preheat and prep: Heat your oven to 400°F (200°C). If you’re using an oven-safe skillet (like a 10–12 inch cast iron), you can bake the dish right in it.

Sauté the aromatics: Warm the olive oil and 2 tablespoons of butter over medium heat. Add onion, carrots, and celery with a pinch of salt. Cook 6–8 minutes until softened. Stir in the garlic and cook 30 seconds.

Make the roux: Add the remaining 2 tablespoons of butter. When melted, sprinkle the flour over the vegetables. Stir constantly for 1–2 minutes to cook off the raw flour taste.

Add the liquids: Slowly whisk in the chicken broth, then the milk or half-and-half. Keep whisking until the mixture is smooth and starting to thicken, 3–5 minutes.

Season and add veggies: Stir in thyme, peas, and corn. Simmer 2–3 minutes, then fold in the shredded chicken and parsley. Taste and season with salt and pepper. The filling should be creamy but not soupy. If too thick, splash in more broth or milk; if too thin, simmer another minute.

Top with biscuits: If your skillet isn’t oven-safe, transfer the filling to a 9x13-inch baking dish. Arrange the biscuits on top, leaving a little space between them so they can rise. Brush with egg wash if using.

Bake: Bake 18–25 minutes, until the biscuits are puffed and deep golden and the filling is bubbling around the edges. If biscuits are browning too fast, tent loosely with foil for the last few minutes.

Rest and serve: Let the pot pie rest 5–10 minutes so the filling settles. Sprinkle with extra parsley and serve warm.