Brown the beef: Heat olive oil in a large oven-safe pot over medium-high heat. Season beef with salt and pepper and brown it in batches, about 2–3 minutes per side. Remove and set aside.

Cook the vegetables: Add the onion and mushrooms to the same pot. Cook for 5–7 minutes, until softened. Add garlic and cook for another minute.

Make the gravy: Stir in tomato paste and flour. Cook for about 1 minute. Slowly add the beef broth while stirring. Add Worcestershire sauce, thyme, and rosemary.

Simmer the beef: Return the beef to the pot. Bring to a simmer, cover, and cook on low for 1–1½ hours, until the beef is very tender and the gravy has thickened.

Cool slightly: Remove from heat and let the filling cool for about 10–15 minutes. This helps keep the pastry from getting soggy.

Add the pastry: Transfer the filling to a 9-inch pie dish if you didn’t cook it in an oven-safe dish. Lay the puff pastry over the top and press the edges around the dish. Cut a few small slits in the center.

Egg wash: Brush the pastry with the beaten egg and water.

Bake: Bake at 400°F for 20–25 minutes, until the pastry is puffed and beautifully golden brown.

Rest & serve: Let the pie rest for 10 minutes before serving.