Place diced potato in a microwave-safe bowl with 1 cup of water. Microwave for 10 minutes or until fork-tender. Drain completely and set aside.
Season chicken thighs with garlic powder and black pepper. Cook in a pan over medium-high heat or simmer in salted water until cooked through, about 15 minutes. Let cool slightly, then shred or cut into bite-sized pieces.
Preheat oven to 375°F (190°C).
In a large bowl, combine the cream of chicken soup and heavy cream. Add the cooked chicken, diced onion, frozen peas and carrots, drained potato, and thyme leaves stripped from the sprig. Season with garlic powder and black pepper. Stir until evenly combined.
Pour the filling into an 8x11 baking dish and spread evenly.
Lay the puff pastry sheets over the filling, overlapping as needed to cover the dish fully. Press the edges down against the rim of the dish. Trim any excess.
Whisk together the egg and 1 tablespoon of water. Brush the pastry evenly with the egg wash. Bake for 20-25 minutes until the pastry is deep golden brown and the filling is bubbling at the edges.
Let rest for 5 minutes before serving.