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 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, cooking for 1 minute to remove the raw flour taste.

Slowly pour in the beef broth while stirring constantly to prevent lumps. Add the Worcestershire sauce and dried thyme. Return the browned beef to the pot and bring to a simmer. Reduce heat to low, cover, and cook 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. Taste and adjust seasoning as needed. Let the filling cool slightly before assembling the pie.

Preheat your oven to 400°F (200°C). Roll out one sheet of pastry to fit your pie dish. Pour the cooled filling into the dish. Cover with the second pastry sheet, crimping the edges to seal. Brush with beaten egg and cut a few slits in the top for steam to escape. Bake for 30-35 minutes until golden brown and bubbling.