Add the squash, butter, sherry, bay leaf and 1 cup of chicken stock to a medium pot over medium heat and bring to a simmer; simmer for 15 minutes. Season with salt and pepper. Let cool for 10 minutes.
Preheat the oven to 425 degrees F.
Add the chicken, vegetable medley and thyme to the squash mixture. If the mixture is too thick, add more chicken stock; season to taste. Pour into a 9-by-13-inch baking dish and top with the Par-Baked Puff Pastry Squares. Bake until the squares are golden brown and the squash mixture is bubbly, 10 to 15 minutes. Let cool for 5 minutes, then top with fresh parsley and serve.
Position an oven rack in the lower third of the oven and preheat to 425 degrees F. Line a baking sheet with parchment.
Cut the pastry sheet into 12 pieces using a pizza cutter and transfer to the prepared baking sheet. Brush with the egg and place in the freezer for 10 minutes.
Bake until puffy and light brown, about 10 minutes.