Step 1: Prepare the filling

Heat a large skillet over medium heat. Add the minced meat and cook until browned, breaking it up with a spoon. Remove the meat from the skillet and set aside.

In the same skillet, add the chopped onion and diced carrot. Cook for 5-7 minutes until softened. Stir in the flour and cook for 1 minute. Return the browned meat to the skillet, then add the beef stock, tomato paste, Worcestershire sauce, salt, and black pepper. Simmer for 10-15 minutes until the mixture thickens. Let it cool.

Step 2: Make the pastry

In a mixing bowl, rub the butter into the flour with your fingertips until the mixture resembles breadcrumbs. Gradually add cold water, 1 tablespoon at a time, mixing until the dough comes together. Wrap the dough in cling film and chill for 20 minutes.

Step 3: Assemble the pie

Preheat the oven to 200°C (180°C fan) or 400°F. Roll out the pastry on a floured surface to fit your pie dish. Place the meat filling in the dish and cover with the pastry. Trim the edges and crimp to seal. Cut a small slit in the center of the pastry to allow steam to escape. Brush the pastry with beaten egg.

Step 4: Bake

Bake the pie in the preheated oven for 25-30 minutes, or until the pastry is golden brown and crisp.

Step 5: Serve

Let the pie cool slightly before serving. Serve hot with your favorite sides.