In a large skillet, heat the vegetable oil over medium heat. Add the finely chopped onion and minced garlic, and sauté until the onion is soft and translucent.
Add the ground beef to the skillet and cook until browned. Drain any excess fat.
Stir in the tomato paste, Worcestershire sauce, ground black pepper, and salt. Cook for a few minutes until well combined.
Sprinkle the flour over the beef mixture and stir well. Gradually add the beef broth, stirring constantly to avoid lumps. Cook for about 10 minutes until the mixture thickens.
Remove the skillet from the heat and let the filling cool to room temperature.
In a large mixing bowl, combine the flour and salt. Add the cold, cubed butter and use a pastry cutter or your fingers to blend the butter into the flour until the mixture resembles coarse crumbs.
Gradually add the cold water, mixing until a dough forms. Turn the dough out onto a lightly floured surface and knead briefly until smooth. Divide the dough into two equal portions and shape each into a disk. Wrap in plastic wrap and refrigerate for at least 30 minutes.
Preheat your oven to 400°F (200°C). Grease a muffin tin or pie dish.
On a lightly floured surface, roll out one disk of dough to about 1/8 inch thick. Cut out circles large enough to line the muffin tin or pie dish. Press the dough into the prepared tin or dish.
Fill the pastry with the cooled meat mixture.
Roll out the second disk of dough and cut out circles to fit as lids on top of the pies. Place the lids over the filling and press the edges to seal. Use a fork to crimp the edges.
Brush the tops of the pies with the beaten egg for a golden finish.
Bake in the preheated oven for 20-25 minutes, or until the pastry is golden brown and crisp.
Allow the meat pies to cool slightly before serving. They can be enjoyed hot or at room temperature.
Enjoy your meal!