Follow these simple steps to create your Skillet Chicken Pot Pie With Puff Pastry:

1. Sauté Chicken: In a large skillet, heat olive oil over medium heat. Add the diced chicken and cook until browned and cooked through, approximately 5-7 minutes. Remove chicken from the skillet and set aside.
2. Cook Vegetables: In the same skillet, add the chopped onion, carrots, and celery. Sauté for about 5 minutes or until the vegetables are softened.
3. Add Garlic and Seasonings: Stir in the minced garlic, thyme, rosemary, salt, and pepper. Cook for an additional minute until fragrant.
4. Thicken: Sprinkle flour over the vegetable mixture and stir well, cooking for about 2 minutes to remove the raw flour taste.
5. Incorporate Liquids: Gradually add chicken broth and heavy cream, stirring constantly until the mixture thickens and bubbles.
6. Return Chicken: Add the cooked chicken and frozen peas to the skillet, stirring until well combined. Remove it from the heat.
7. Preheat Oven: While the filling cools slightly, preheat your oven to 400°F (200°C).
8. Add Puff Pastry: Roll out the puff pastry sheets and lay one sheet on top of the skillet. Trim any excess pastry, and score the top lightly for decoration and steam venting.
9. Brush with Egg Wash: Brush the pastry with the beaten egg for a golden finish.
10. Bake: Transfer the skillet to the preheated oven and bake for about 20-25 minutes, or until the pastry is golden brown and puffed.
11. Cool Slightly: Allow to cool for a few minutes before serving to let the filling set.

These straightforward instructions will guide you in creating this wonderful dish effortlessly.