01 - Set the oven to 350°F and allow it to fully heat.
02 - Heat 1 tablespoon olive oil in a large heavy-based pan over medium-high heat. Brown the beef in batches and set aside on a plate.
03 - Add remaining olive oil to the pan. Cook the onion, carrots, and celery for 5 minutes until softened.
04 - Stir in minced garlic and cook for 1 minute. Add tomato paste and flour, cooking for 2 minutes while stirring constantly.
05 - Gradually pour in beef stock, scraping up browned bits from the pan. Stir in Worcestershire sauce, thyme, rosemary, bay leaves, then return beef. Season with salt and pepper.
06 - Bring mixture to a simmer, cover, and cook gently for 1.5 hours, stirring occasionally until beef is tender and gravy thickens. Remove bay leaves and cool filling.
07 - Spoon the cooled beef filling into a 1.5-quart pie dish.
08 - Roll out pastry to fit the pie dish. Cover the filling, trim excess pastry, crimp edges to seal, and cut a small steam vent in the center.
09 - Brush the pastry with beaten egg and bake for 30 to 35 minutes until golden and crisp.
10 - Allow the pie to rest for 5 minutes before serving.