1. Preheat oven to 400°F (200°C).

2. In a 10 to 12 inch cast iron skillet, melt butter over medium heat.

3. Add onion, carrots and celery and sauté until softened.

4. Stir in flour and cook until pale golden to form a roux.

5. Gradually whisk in chicken broth and milk until smooth and thickened.

6. Season with thyme, garlic, salt and pepper.

7. Fold in shredded chicken and peas, stirring gently to combine.

8. Spread filling evenly in the skillet.

9. Drape puff pastry sheet over filling, trim excess and seal edges.

10. Brush pastry with beaten egg.

11. Cut small slits in pastry to vent steam.

12. Bake for 25 to 30 minutes until crust is golden and puffed.

13. Let rest 5 to 10 minutes before serving to allow filling to set.

14. Serve warm directly from the skillet.