01 - Preheat the oven to 400°F.
02 - Season beef cubes with salt and pepper. In a large Dutch oven or heavy pot, heat olive oil over medium-high heat. Brown beef in batches, transferring to a plate as browned.
03 - Reduce heat to medium; add onion, garlic, carrots, celery, and mushrooms. Sauté until softened, about 7 minutes.
04 - Stir in tomato paste and flour; cook for 1 minute.
05 - Return beef to pot. Add beef broth, red wine, Worcestershire sauce, thyme, rosemary, and bay leaf. Stir well and bring to a simmer.
06 - Cover and cook on low heat for 1 hour, stirring occasionally, until beef is tender and sauce has thickened. Discard bay leaf.
07 - Stir in frozen peas and adjust seasoning if needed.
08 - Transfer filling to a 9-inch deep-dish pie dish or ovenproof casserole.
09 - Roll puff pastry to fit over the dish. Place pastry over filling, trim edges, and press to seal. Cut a few small slits in the top to vent steam.
10 - Brush pastry with beaten egg.
11 - Bake for 25 to 30 minutes, until pastry is golden brown and filling is bubbling.
12 - Let cool for 10 minutes before serving.