01 - Preheat oven to 400°F.
02 - Heat olive oil in a large Dutch oven or deep skillet over medium-high heat. Brown beef cubes in batches, seasoning lightly with salt and pepper. Remove beef and set aside.
03 - Add onion, carrots, celery, and mushrooms to the pot. Cook for 5 minutes, stirring occasionally, until vegetables soften. Add garlic and cook 1 minute more.
04 - Stir in tomato paste, then sprinkle flour over vegetables and stir well to coat.
05 - Pour in red wine, scraping up browned bits from bottom. Add beef broth, Worcestershire sauce, thyme, and bay leaf. Return beef and juices to pot. Bring to simmer, cover, and cook for 1 hour, stirring occasionally, until beef is tender.
06 - Remove bay leaf. Stir in peas. Taste and adjust seasoning with salt and pepper.
07 - Transfer beef mixture to a deep 9-inch pie dish or similar baking dish.
08 - Roll out puff pastry to fit over top of dish. Place pastry over filling, pressing edges to seal and trimming excess. Cut small slits in pastry to allow steam to escape.
09 - Brush pastry with beaten egg.
10 - Bake for 25-30 minutes, or until pastry is golden and crisp. Let stand for 10 minutes before serving.