Allow puff pastry to thaw at room temperature for 45 minutes and then gently unfold.
In a large pot, melt butter over medium high heat. Add onion, celery, carrot, and salt and sauté until onions are translucent and vegetables start to get tender. Sprinkle flour over vegetables and cook for 1-2 minutes. Gradually whisk in milk, heavy cream and Better Than Bullion chicken base and bring to a slow boil. Simmer gently over medium heat until sauce begins to thickens, about 5 minutes. Turn heat to low, and add chicken, peas, corn, parmesan cheese, if using, and fresh thyme; stir to combine.
Preheat oven to 400°F.
Pour chicken mixture into a 9 x 9 baking dish or 6 individual small cast iron skillets or ramekins.
If using a 9x9 baking dish, then roll out 1 sheet frozen puff pastry (thawed), over a lightly floured surface (about ½ -inch extra on all 4 sides of your pan). Place the puff pastry on top of the chicken filling and cut 2 to 3 slits on top, for steam to escape.
If using individual skillets/ramekins, then roll out 1 sheet frozen puff pastry (thawed), over a lightly floured surface and cut into 24 small rectangle pieces. Place 4 strips on top of the chicken filling leaving the middle uncovered, for the steam to escape.
In a small bowl combine the whisked egg with 1 tablespoon of water and brush the top of the puff pastry. Bake for 30-35 minutes, or until the top of the puff pastry is golden brown in color.
Cool for 5 minutes before serving. Enjoy!