- Preheat the oven to 400℉ 
- In a 12-inch cast iron skillet, melt butter over medium heat. Add onion, carrot, and celery. Cook until veggies are soft and onion is translucent, about 5-6 minutes. Add minced garlic and thyme and saute until fragrant, 1 minute. 
- Sprinkle flour over the veggies and stir to coat. Cook and sauté, 1-2 minutes. Whisk in chicken broth, stir to avoid lumps. 
- Once smooth, stir in milk. Bring to a low simmer and cook until just starting to bubble and thicken, about 3-4 minutes. 
- Remove skillet from heat, and stir in shredded chicken, frozen peas, salt and pepper and gently fold to combine.  
- On a lightly floured surface, roll one sheet of puff pastry into a 16-inch square. Cut into 3-inch squares (you should have about 16-20 pieces). Arrange the squares on top of the chicken mixture, overlapping slightly.  In a small bowl, beat the egg with 1 tablespoon of water. Brush the pastry with the egg wash.  
- Bake for 25–30 minutes, or until the puff pastry is deep golden brown and crisp. 
- Let rest for 10ish minutes before serving - it will be hot! Spoon directly from skillet.