Preheat the oven to 400 degrees F. Grease a 9x13-inch baking dish; set aside.
Roll out each pastry sheet on a lightly floured surface, shaping them into 9x13-inch rectangles (or size to your baking dish). Cut one of the sheets crosswise into six 2-inch strips and the remaining sheet lengthwise into five 2-inch strips.
Arrange the strips in a close weave pattern on a baking sheet to form a 9x13-inch lattice to fit your baking dish. Freeze the lattice while preparing the filling.
Heat butter in a medium skillet over medium heat. Sauté the onion until it becomes tender, about 5-7 minutes. Add the garlic and herbs to the skillet, cooking for an additional minute.
Blend in the flour, stirring constantly for about a minute until well mixed. Gradually pour in the broth and 1 cup of cream while stirring continuously.
Bring the mixture to a boil, maintaining constant stirring. Let it cook and thicken, stirring occasionally, for about 2 minutes.
Stir in the chicken, vegetables, salt, and pepper, bringing the mixture back to a boil.
Spread the filling into the bottom of the prepared baking dish. Arrange the lattice over the top of the filling, trimming it to fit the dish.
Whisk together the egg yolk and the remaining cream, then brush it over the pastry lattice. Bake the dish uncovered until the filling bubbles and the pastry turns golden brown, about 45-55 minutes. If the pastry starts browning too quickly, loosely cover it with foil.
Allow the pot pie to stand for 15 minutes before serving.