Season the beef cubes generously with salt and pepper. Heat olive oil in a large Dutch oven or heavy-bottomed pot over medium-high heat. Brown the beef in batches, ensuring each piece gets a nice sear on all sides.

Reduce heat to medium and add the onions, carrots, and celery to the same pot. Cook for 5-7 minutes until vegetables begin to soften. Add the minced garlic and cook for another minute until fragrant.

Sprinkle the flour over the vegetables and beef, stirring constantly for 2 minutes to cook off the raw flour taste. Gradually pour in the beef broth while stirring continuously to prevent lumps. Add the thyme and Worcestershire sauce. Bring to a simmer, then reduce heat to low, cover, and cook for 1.5-2 hours until beef is fork-tender.

Preheat your oven to 400°F (200°C). Stir the frozen peas into the beef mixture. Roll out one sheet of pastry to fit your pie dish. Pour the beef filling into the dish, then cover with the second pastry sheet. Crimp the edges to seal and brush with beaten egg. Cut a few slits in the top to allow steam to escape.

Bake for 30-35 minutes until the crust is golden brown and the filling is bubbling. Let the pie rest for 10-15 minutes before serving to allow the filling to set.