01 - Heat oven to 350°F.
02 - Heat 1 tablespoon olive oil in a large heavy-based pan over medium-high heat. Season beef with salt and pepper, brown in batches, then remove and set aside.
03 - Add remaining oil to the pan. Cook onion, garlic, and carrots for 5 minutes until softened.
04 - Stir in mushrooms and cook 5 minutes until moisture releases.
05 - Return beef to pan. Stir in tomato paste and flour, cooking for 2 minutes to coat ingredients.
06 - Pour in beef stock and wine, scraping pan to loosen browned bits. Add thyme and Worcestershire sauce. Bring to a simmer.
07 - Cover and cook over low heat for 1.5 hours until beef is very tender. Remove lid during the last 30 minutes to reduce sauce as needed. Adjust seasoning.
08 - Transfer filling to a 9-inch pie dish. Let cool for 20–30 minutes.
09 - Raise oven temperature to 400°F.
10 - Cover cooled filling with puff pastry, trimming excess. Press edges to seal and cut small slits on top for steam.
11 - Brush pastry surface evenly with beaten egg.
12 - Bake for 30–35 minutes until pastry is crisp and golden.
13 - Allow pie to rest for 10 minutes before slicing.