Preheat and prep: Preheat your oven to 400°F (200°C). If your skillet isn’t oven-safe, plan to transfer the filling to a baking dish before adding biscuits.
Sauté the veggies: In a large oven-safe skillet, heat butter and olive oil over medium heat.
Add onion, carrots, and celery. Cook 6–8 minutes, stirring, until softened. Add garlic, thyme, and poultry seasoning; cook 30 seconds until fragrant.
Make the roux: Sprinkle flour over the vegetables.
Stir to coat and cook 1–2 minutes. This cooks out the raw flour taste and thickens the sauce later.
Add liquids: Slowly whisk in chicken broth, scraping up any browned bits. Whisk in milk or half-and-half.
Bring to a gentle simmer and cook 3–5 minutes until thickened and creamy.
Add chicken and veggies: Stir in the chicken, peas, and corn. Season with salt and pepper. Simmer 2–3 minutes to heat through.
If the mixture seems too thick, add a splash of broth; if too thin, simmer another minute.
Taste and adjust: Stir in parsley and taste. Add more salt, pepper, or thyme as needed. The filling should be well-seasoned and slightly creamy.
Top with biscuits: Arrange biscuit dough evenly over the filling, spacing slightly apart.
Brush tops with beaten egg for shine, if using.
Bake: Transfer the skillet to the oven. Bake 12–16 minutes, until biscuits are puffed and deep golden and the filling is bubbling around the edges.
Rest and serve: Let it rest 5 minutes. The filling will thicken slightly as it cools, making it easier to scoop.
Serve warm.