Preheat oven to 400°F (200°C). In large pot of boiling salted water, cook carrots and potato for 4 to 5 minutes or until almost tender-crisp; drain well.
In 9-inch (23 cm) cast iron skillet, melt butter over medium heat; cook onion, garlic and celery for about 5 minutes or until tender. Add carrots, potato, thyme, salt and pepper; sauté for 5 minutes. Sprinkle with flour; cook for 1 to 2 minutes. Whisk in milk, chicken broth and mustard; bring to boil. Reduce heat and simmer for 5 minutes or until slightly thickened. Stir in chicken and peas until incorporated.
On lightly floured surface, roll out pastry into a 10-inch (25 cm) square. Place pastry over filling, pressing edges to adhere to side of skillet. Brush egg over top of pastry. Bake for about 30 minutes or until pastry is golden and filling is bubbling. Let stand for 5 minutes before serving.
This classic, one-pan meal is perfect for those nights when you want to treat your family to something delicious and hearty without the big cleanup. For added creaminess, add a generous dollop of sour cream!