Reduce the heat to medium. Add the bacon and cook, stirring occasionally, until crisp, 6 to 8 minutes. Add to the bowl with the beef. Pour off the excess fat in the pot. Increase the heat to medium-high, add the mushrooms and cook, stirring occasionally, until tender, about 5 minutes. Add to the bowl with the beef. Add the carrots and potatoes, cook for about 5 minutes and add to the bowl.
Return the pot to medium heat and melt the butter. Stir in the flour and cook, stirring constantly, 2 to 3 minutes. Whisk in the wine and demi-glace and cook for 1 minute. Slowly whisk in the stock and bring to a simmer. Add the, beef, bacon, mushrooms, carrots and potatoes. Stir. Add the thyme, bay leaf and pearl onions. Lightly season with salt and pepper. Cover the pot, transfer to the oven and cook until the beef is fork-tender, 2 to 2 1/2 hours. Discard the bay leaf and spoon the excess fat off the cooking liquid. Stir in the parsley.
Increase the oven temperature to 400°F.
Place the puff pastry sheet on a lightly floured work surface. Slightly roll out to an 11 x 11-inch square. Using a sharp knife, score the pastry with diagonal lines about 2 inches apart, forming a diamond pattern. Brush the pastry with the egg mixture. Cut the pastry into 4 equal squares. Place the pastry, egg wash side up, over the bowls and press the edges to seal. Repeat for remaining pastry to make 4 additional pies.
Inspired by Williams-Sonoma Kitchen