Preheat and prep: Heat the oven to 400°F. Grease a 9x13-inch baking dish.
Sauté the vegetables: Melt butter with olive oil in a large skillet over medium heat. Add onion, carrots, and celery. Cook 6–8 minutes until softened. Stir in garlic and cook 30 seconds.
Build the roux: Sprinkle in the flour. Stir constantly for 1–2 minutes until the flour smells toasty and coats the vegetables.
Whisk in the liquids: Slowly pour in chicken broth while whisking to avoid lumps. Simmer 3–4 minutes until the mixture thickens to gravy. Stir in heavy cream and Dijon. Season with salt, pepper, thyme, and parsley.
Add chicken and peas: Stir in cooked chicken, peas, and corn. Taste and adjust seasoning. The filling should be creamy and well-seasoned.
Assemble the casserole: Transfer the filling to the baking dish. Top with puff pastry (trim edges), a pie crust (vent with slits), or biscuit rounds (leave space between).
Finish the top: Brush pastry or crust with egg wash for a shiny, golden finish. Skip if using biscuits.
Bake: Bake 25–35 minutes, until the topping turns deep golden and the filling bubbles around the edges. If the top browns too fast, tent with foil.
Rest and serve: Let the casserole sit 10 minutes so the sauce sets. Scoop and serve warm.
Keep pastry cold: Cold dough puffs higher and flakes better.
Thickness check: The sauce should coat the back of a spoon. If too thick, splash in more broth. If too thin, simmer 2–3 minutes.
Season in layers: Taste after adding cream and chicken. A pinch more salt often unlocks the flavors.