01 - Set the oven temperature to 400°F.
02 - Heat butter and olive oil in a large skillet over medium heat. Add diced onion and minced garlic; sauté for 2 to 3 minutes until softened and fragrant.
03 - Incorporate diced carrots and celery; cook for 5 minutes, stirring occasionally until vegetables begin to soften.
04 - Add frozen peas, corn, and cooked chicken. Sprinkle in thyme, sage, salt, and black pepper; stir to combine evenly.
05 - Sprinkle all-purpose flour over the mixture. Cook while stirring constantly for 2 minutes to create a roux base.
06 - Gradually pour in chicken broth while stirring to prevent lumps. Add milk or cream and bring to a gentle simmer. Continue cooking for 5 to 7 minutes until the sauce thickens.
07 - Remove skillet from heat. Taste the filling and adjust salt or pepper as necessary.
08 - Transfer the filling into a 9-inch pie dish or a similarly sized baking vessel.
09 - If necessary, roll out the puff pastry to cover the pie dish. Place pastry sheet atop the filling, trim the edges, and crimp them securely. Cut small vents for steam release.
10 - Brush the pastry surface with the beaten egg to promote a golden finish.
11 - Bake in the preheated oven for 25 to 30 minutes until the crust is golden brown and the filling bubbles visibly.
12 - Allow the pot pie to cool for 10 minutes prior to portioning and serving.