01 - Set oven temperature to 350°F.
02 - Toss beef cubes with flour, salt, and pepper.
03 - Heat olive oil in a heavy-bottomed pot over medium-high heat; brown beef in batches and set aside.
04 - In the same pot, soften onion for 4 minutes, then add garlic and cook for 1 minute.
05 - Add mushrooms and carrots; cook while stirring for 5 minutes until mushrooms release liquid and begin browning.
06 - Stir in tomato paste and cook for 1 minute; return beef to pot.
07 - Pour in beef broth and red wine; add Worcestershire sauce, thyme, and bay leaf; stir and bring to simmer.
08 - Cover pot, place in oven, and cook for 1½ hours until beef is tender.
09 - Remove bay leaf, adjust seasoning to taste, and allow filling to cool to room temperature.
10 - Raise oven temperature to 400°F.
11 - Roll out puff pastry to fit a 9-inch pie dish.
12 - Fill dish with cooled beef mixture; cover with pastry, trim and crimp edges, and cut slits for steam release.
13 - Brush the pastry top with beaten egg.
14 - Bake for 30 to 35 minutes until pastry is golden and puffed.
15 - Allow pie to rest for 10 minutes before slicing and serving.