In a heavy Dutch oven over medium heat, render bacon in the vegetable oil until lightly browned and beginning to crisp. Using a slotted spoon, transfer the bacon to a large bowl and set aside. Season the meat with the salt and pepper, and brown in the bacon fat, in batches if necessary and turning often to promote even cooking. When the meat is browned on all sides, transfer the pieces to the bowl with the bacon. (If the bits on the bottom of the pan begin to burn, deglaze with a bit of water or some of the wine, and scrape the bottom of the pan with a wooden spoon to remove all browned bits. Transfer this liquid to the bowl along with the beef. ) When all of the beef is browned, add the chopped onions and carrots to the Dutch oven and cook, stirring frequently, until browned around the edges, about 8 to 10 minutes. Transfer the browned vegetables to another bowl and set aside. Deglaze the pan with 1 cup of water and transfer this liquid along with the released browned bits to the bowl with the browned meat. Add 3 tablespoons of the butter to the Dutch oven and stir in the flour and cook until the flour is reddish-brown, about 6 to 8 minutes. Add the tomato paste, stir to combine, then slowly whisk in the stock and 3 cups of the wine. Bring to a simmer and cook until slightly thickened, about 5 minutes. Using a large piece of cheesecloth, make a bundle containing the reserved caramelized veggies, parsley stems, thyme sprigs, bay leaves, garlic and peppercorns and secure with a piece of kitchen twine. Add this to the pot, along with the reserved bacon and browned meat. Cover the pot and simmer very slowly for 2 1/2 to 3 hours, or until the beef is very tender.

Remove the cheesecloth bundle from the sauce and set in a strainer over a medium bowl. Press down on the bundle with the back of a spoon and transfer any accumulated liquids to the Dutch oven. Discard the cheesecloth bundle.

Using a slotted spoon or tongs, transfer the meat to a medium bowl and set aside. Using a large spoon, skim any fat from the surface of the sauce. Increase the heat to medium-high, and cook the sauce until it reduces to heavy cream consistency, about 20 minutes, stirring occasionally so that sauce does not burn on the bottom of the pot.

While the sauce is reducing combine the pearl onions, remaining tablespoon of butter, sugar and 1 cup of water in a large skillet and bring to a boil over high heat. Cover, reduce heat to medium and simmer for about 3 minutes. Stir in the mushrooms, cover the pan, and cook for another minute or two, until the mushrooms have given up their liquid. Add the baby carrots and turnips, cover, and continue to cook until the vegetables are crisp-tender, about 8 to 10 minutes. Remove the cover and cook, shaking the pan frequently, until the vegetables are tender and golden brown. Transfer to the sauce and add the remaining cup of red wine and cognac and continue to cook until the sauce is thickened and coats the back of a spoon. Add the parsley and reserved beef, stir to combine well, then set aside to cool.

When the filling has cooled completely, divide the filling evenly among 6 (2-cup) ramekins.

Preheat the oven to 400 degrees F. On a lightly floured work surface, roll out 1 sheet of puff pastry to measure 12 by 12-inches. Using a small plate or cup saucer just slightly wider than the rim of the ramekins as a guide, cut out 4 circles of pastry by running the tip of a sharp knife around the edge of the guide. Repeat with the second sheet of puff pastry, but only cut 2 circles out of this sheet and save the remaining puff pastry for another project.

In a small bowl using a fork, beat the egg lightly. Using a pastry brush, lightly coat the edges of each circle of pastry with some of the beaten egg. Top each ramekin with 1 of the pastry circles, egg side down, and fit the edges around the rim of the ramekin with your fingers. Press to seal well. Using the tip of a sharp knife, cut a few decorative vent holes in the top of the pastry circle. Repeat with the remaining ramekins and pastry circles. Using a pastry brush, brush some of the remaining egg over the tops of each pastry circle.

Place the ramekins in the middle of the oven and bake until the puff pastry is puffed and golden and the filling is bubbly and hot throughout, about 20 to 25 minutes. Serve immediately.