Add the beef to a large bowl. Sprinkle it with the flour, season with salt and black pepper and toss to coat.
Heat 1 tablespoon of olive oil in a heavy pot over medium-high heat. Brown half the beef for about 5 minutes, turning the pieces. Transfer it to a plate. Add the remaining tablespoon of oil and brown the rest of the beef, then transfer it to the plate.
Add the onion, quartered mushrooms, rosemary and garlic to the pot. Cook for about 5 minutes, stirring occasionally.
Return the beef and any juices to the pot. Stir in the beef broth and tomato paste. Bring to a simmer, then reduce the heat and cover. Cook gently for 1 hour.
Uncover and simmer for about 30 minutes more, until the beef is tender and the gravy has reduced. If the beef is still chewy, continue cooking gently and check again. Season to taste with salt and black pepper.
Divide the filling between shallow containers and refrigerate promptly. Chill for at least 2 hours, until cold. You can prepare it a day ahead.
Heat the oven to 410°F (210°C). Cut each shortcrust sheet diagonally in half and fit one triangle into each of the 4 pie pans, covering the base and sides. Leave a little pastry above the rim and trim as needed.
Brush the edges of the shortcrust with beaten egg. Divide the cold filling evenly among the pastry-lined pans.
Cut each puff pastry sheet diagonally in half. Lay one triangle over each pie, trim the excess and press the edges together with a fork to seal. Brush the lids with the remaining egg and cut a small cross in the center of each.
Set the pans on a baking sheet and bake for about 30 minutes, until the lids are puffed and golden. Let the pies stand briefly before serving.
