In a large skillet, melt butter over medium heat. Add onion, carrot, celery, thyme, salt and pepper, cooking for 5 to 6 minutes or until vegetables are tender.
Sprinkle flour over the vegetables and cook, stirring, for 1 minute. Gradually whisk in milk and chicken broth. Stirring constantly, cook for 8 to 10 minutes or until mixture begins to simmer and thickens. Stir in broccoli, chicken, mustard and nutmeg; return to simmer. Remove from heat and stir in 1 1/2 cups of the cheese.
Preheat oven to 425°F.
Divide filling among six 1-cup ramekins; let cool slightly. Place pastry on lightly-floured surface and cut into six equal squares. Place one piece of pastry atop each ramekin, pressing gently to adhere. Beat egg with 1 tbsp water and brush lightly over the pastry. Cut two steam vents in the centre of each pie. Sprinkle the remaining cheese on top of the puff pastry.
Place ramekins on a parchment-lined baking sheet. Bake for 20 minutes, or until filling is bubbling and pastry is golden brown. Let stand for 5 minutes before serving.
Notes
Tip: This dish is also delicious when made with dried or fresh rosemary instead of thyme.Recipe courtesy of Armstrong Cheese.