01 - Set the oven to 350°F (180°C) to prepare for baking.
02 - Heat 1 tablespoon of olive oil in a large heavy-based skillet over medium-high heat. Brown the beef in batches, transferring cooked pieces to a plate.
03 - Add remaining olive oil to the pan, then cook onion, carrots, and celery for 5 minutes until softened.
04 - Stir in minced garlic, cooking for 1 minute. Incorporate tomato paste and flour, cooking for 2 minutes while stirring steadily.
05 - Gradually pour in beef stock, scraping any browned bits from the pan. Stir in Worcestershire sauce, thyme, rosemary, and bay leaves. Return beef to the pan, 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 allow filling to cool.
07 - Transfer the beef filling into a 1.5-quart pie dish.
08 - Roll out pastry to fit the dish top. Cover filling with pastry, trim excess, and crimp edges to seal. Cut a small steam vent in the center.
09 - Brush 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 slicing and serving.