Heat olive oil in a large Dutch oven over medium-high heat. Season the beef cubes with salt and pepper, then brown them in batches until nicely seared on all sides. Remove the beef and set aside.

In the same pot, add the onions, carrots, and celery. Cook for 5-7 minutes until softened. Add the minced garlic and cook for another minute until fragrant.

Sprinkle the flour over the vegetables and stir to coat. Cook for 1 minute to remove the raw flour taste. Gradually add the beef broth while stirring constantly to prevent lumps. Add the Worcestershire sauce and dried thyme.

Return the browned beef to the pot. Bring to a simmer, then reduce heat to low, cover, and cook for 1.5-2 hours until the beef is fork-tender. Stir in the frozen peas during the last 5 minutes of cooking.

Preheat your oven to 400°F (200°C). Transfer the beef filling to a 9-inch pie dish. Roll out one sheet of pastry to fit over the top of the dish. Brush the edges with water and place the pastry over the filling, pressing to seal. Cut a few slits in the top to allow steam to escape. Brush with beaten egg for a golden finish.

Bake for 25-30 minutes until the crust is golden brown and the filling is bubbling. Let the pie rest for 10 minutes before serving to allow the filling to set.