01 - Preheat oven to 350°F. Heat vegetable oil in a large Dutch oven over medium-high heat. Brown beef in batches, setting aside browned cubes.
02 - Add onion, carrot, and celery to the pan and cook for 5 minutes until softened. Stir in garlic and cook for 1 minute more.
03 - Blend in tomato paste and flour, cooking while stirring constantly for 2 minutes.
04 - Return browned beef to the pan. Add beef stock, red wine, Worcestershire sauce, thyme, bay leaf, salt, and pepper. Stir, scraping browned bits from the bottom.
05 - Cover and transfer the pan to the oven. Cook for 1 hour until beef is tender and sauce has thickened. Remove bay leaf and let filling cool for 20 minutes.
06 - Increase oven temperature to 400°F.
07 - Transfer cooled filling to a 9-inch pie dish. Roll out puff pastry to cover the filling, trim excess, and seal edges by crimping. Cut small slits in pastry for steam release.
08 - Brush the puff pastry surface with beaten egg to achieve a golden finish.
09 - Bake for 30 to 35 minutes until the pastry is golden and crisp.
10 - Allow pie to cool for 10 minutes prior to slicing and serving.