Preheat oven to 200°C (400°F).
In a large skillet, melt butter with olive oil. Add the onion, garlic, and carrots. Cook until soft, about 5 minutes.
Sprinkle the flour over the vegetables and stir for 1 minute to cook out the raw taste.
Slowly pour in the chicken stock while stirring constantly, then add milk or cream. Let it simmer until slightly thickened.
Add cooked chicken, peas, thyme, salt, and pepper. Mix well and cook for another 2–3 minutes.
Spoon the mixture into a baking dish or small ramekins.
Cover with puff pastry, trimming the edges neatly. Cut small slits in the top to let steam escape.
Brush the top with a beaten egg for that golden crust.
Bake for 25–30 minutes until the pastry is puffy and golden.
Let it rest for 5 minutes before serving.