To begin, heat the olive oil in a large saucepan over medium heat. Add the chopped onion and diced carrots, and sauté until they begin to soften.

This should take around 5 minutes. Next, add the minced garlic and continue to cook for another minute until fragrant.

Increase the heat to medium-high and add the diced beef to the pan. Brown the meat on all sides, which should take about 10 minutes.

Once browned, stir in the Worcestershire sauce, dried thyme, and rosemary. Pour in the beef stock and bring to a simmer. Season with salt and pepper to taste.

Cover the saucepan and reduce the heat to low, allowing the mixture to simmer gently for about 1.5 hours.

The beef should become tender during this time. Once cooked, remove the lid and let the filling cool slightly.

While the filling cools, preheat your oven to 200°C (180°C fan). Roll out the puff pastry on a lightly floured surface to a thickness of about 5 mm.

Transfer the cooled filling to a pie dish, then cover it with the rolled pastry, sealing the edges well. Cut a small cross in the centre of the pastry to allow steam to escape.

Brush the top with the beaten egg to achieve a golden finish. Place the pie in the preheated oven and bake for 25-30 minutes, or until the pastry is golden brown.

Serve hot and enjoy your delicious steak pie!