In a large saute pan, heat the olive oil over medium-high heat and when hot add the ground beef and cook until lightly browned on both sides, about 2 to 3 minutes per side. Transfer the beef to a bowl and set aside.

Add the onions and carrots and a pinch of salt and cook until the vegetables are soft, about 5 minutes. Add the garlic and the tomato paste and continue to cook, stirring, for another 5 minutes. Add the beef and any juices that have accumulated back to the pan, as well as, the beef stock, all but 1 tablespoon of the beer, Worcestershire and thyme. Bring to a boil, reduce the heat to medium-low, cover and simmer for 35 minutes.

In a small bowl combine the cornstarch with the remaining tablespoon of beer or water and mix well. Remove the cover from the pan, add the cornstarch slurry, stir well and continue to cook, stirring occasionally, until the mixture thickens, about 25 minutes longer. Allow the mixture to cool completely before filling the pies. The filling can be made ahead and refrigerated for up to three days.

To make the pies:

Preheat the oven to 400º F.

Lightly flour your work surface and roll out the puff pastry to about 1/8-inch thick, (roughly a rectangle that is 14"x12"). Cut out 12 4-inch rounds using a circular pastry cutter. Transfer the rounds to a standard muffin tin, pressing gently against the sides, so that the pastry comesup to the top of the tin and slightly over. Spoon 1/3 cup of the filling into each well of the muffin tin. Spoon 1 tablespoon of the cheese on top of the filling. 

Roll the remaining puff pastry to the same thickness and cut out 12 3 1/2-inch rounds for the tops. Place the smaller circle on top and press the dough together to form a seal. Using a small pairing knife cut a small slit in the top of each pie. Brush the pies with the egg wash and refrigerate for at least 15 minutes and up to an hour.

Place the muffin pan on a baking sheet. Bake the pies until bubbly and golden brown, about 18 to 20 minutes.

Note: Any remaining filling and/or puff pastry can be used to make hand pies or more using the muffin pan once it is cooled.