Preheat oven to 400 degrees F.
In a small bowl, whisk together egg and water. Set aside.
In heavy pan or skillet, melt butter. Saute carrots, onions, celery and garlic until vegetables are softened; about 6-8 minutes. Season lightly with salt and pepper.
Form a roux: Stir ground thyme and flour into vegetables until well combined. Allow to cook for about 2-3 minutes until flour melts and is bubbly.
Add stock and milk to pan. Stir for 2-3 more minutes until mixture thickens to a gravy like consistency. If needed, season with more thyme, salt and/or pepper.
Turn off heat and stir in the frozen peas and chicken.
Transfer mixture to a baking dish. Lightly lay the puff pastry (either as a full sheet or in a lattice) on top of the vegetable mixture.
Carefully, brush egg wash on the puff pastry. Optional: Sprinkle on salt flakes prior to baking.
Bake pot pie for 15- 20 minutes until pastry puffs and is golden brown.