01 - Set oven temperature to 350°F.
02 - Heat 1 tablespoon olive oil in a large heavy pan over medium-high heat. Season beef with salt and pepper, brown in batches, then remove and set aside.
03 - Add remaining olive oil to pan and cook onion, garlic, and carrots for 5 minutes until softened.
04 - Stir in mushrooms and cook an additional 5 minutes until moisture is released.
05 - Return beef to pan, mix in tomato paste and flour, cooking for 2 minutes.
06 - Pour in beef stock and wine, scraping browned bits from the pan. Add thyme and Worcestershire sauce, then bring to a simmer.
07 - Cover and cook over low heat for 90 minutes until beef is tender. Remove lid for last 30 minutes to thicken sauce. Adjust seasoning.
08 - Transfer filling to 9-inch pie dish and let cool for 20 to 30 minutes.
09 - Raise oven heat to 400°F.
10 - Cover filling with puff pastry, trim excess, seal edges and cut small slits for steam to escape.
11 - Brush beaten egg over pastry surface.
12 - Bake for 30 to 35 minutes until pastry is golden and crisp.
13 - Allow pie to rest 10 minutes before slicing and serving.