Step 1: Prepare the Chicken and Vegetables : If using raw chicken, poach it in lightly salted water for 10–12 minutes or until cooked. Shred or dice and set aside. In a large skillet, heat butter and olive oil over medium heat. Add onions, garlic, carrots, and celery; sauté for 5–7 minutes until softened. Add potatoes (if using) and cook for another 5 minutes.

Step 2: Make the Creamy Filling : Sprinkle flour over the sautéed vegetables and stir for 1–2 minutes to remove the raw flour taste. Slowly pour in the chicken broth while whisking constantly to avoid lumps. Add milk or cream and bring to a gentle simmer until the mixture thickens (about 5–7 minutes). Stir in shredded chicken, peas, thyme, rosemary, salt, and pepper. Taste and adjust seasoning. The filling should be rich and creamy. Remove from heat and let it cool slightly.

Step 3: Assemble the Pot Pie : Preheat oven to 400°F (200°C). Pour the chicken filling into a 9-inch pie dish or divide into individual ramekins. Roll out the puff pastry slightly to fit over your dish. Drape the puff pastry over the filling, trimming the edges if needed. Press the edges gently to seal and cut small slits on top to allow steam to escape. Brush the pastry with beaten egg for a glossy, golden finish.

Step 4: Bake : Place the dish on a baking tray (to catch any drips) and bake for 25–30 minutes, or until the pastry is puffed and golden brown. Let it cool for 10 minutes before serving—this allows the filling to set slightly.