Preheat the oven:
Preheat to 190°C (375°F). Grease a medium ovenproof pie dish.

Cook the filling:
In a large pan, melt butter over medium heat. Sauté onion and garlic for 2–3 minutes. Add carrots and cook for 5 minutes until starting to soften. Stir in flour and cook for 1 minute, then slowly add stock and milk, whisking until smooth and thickened.

Add chicken and peas:
Stir in the cooked chicken (or vegetables), peas, salt, pepper, and thyme. Simmer for 2–3 minutes. Remove from heat and let cool slightly.

Assemble the pie:
Spoon the filling into the prepared dish. Lay the puff pastry over the top and trim any excess. Press the edges to seal, and cut a few small slits in the top to allow steam to escape. Brush with beaten egg.

Bake:
Bake for 30–35 minutes or until the pastry is puffed and golden brown.

Rest and serve:
Let rest for 5–10 minutes before serving. Enjoy with a green salad or steamed veggies.