Heat olive oil in a large Dutch oven or heavy-bottomed pot over medium-high heat. Season the beef cubes with salt and pepper, then brown them in batches, about 3-4 minutes per side. 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 whisk in the beef broth, Worcestershire sauce, thyme, and rosemary. Bring to a simmer, then return the beef to the pot.

Reduce heat to low, cover, and simmer for 1.5-2 hours until the beef is fork-tender. Stir in the frozen peas and corn during the last 10 minutes of cooking. The filling should be thick and rich.

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 the top of the dish. Place it over the filling, trim the edges, and crimp to seal. Cut a few slits in the top to allow steam to escape. Brush with beaten egg for a golden finish.

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.