1. Preheat the oven to 400°F and line a baking sheet with parchment paper.

2. Heat olive oil in a large skillet over medium heat, then cook the onion and carrot for 4 to 5 minutes until softened.

3. Add the garlic and cook for 30 seconds until fragrant.

4. Add the ground beef and cook for 6 to 8 minutes, breaking it apart, until browned and fully cooked. Drain excess fat if needed.

5. Stir in tomato paste, Worcestershire sauce, paprika, thyme, salt, and black pepper, then cook for 1 minute.

6. Sprinkle in the flour and stir until the beef mixture is evenly coated.

7. Pour in the beef broth, add the peas, and simmer for 3 to 5 minutes until the filling thickens.

8. Remove the skillet from the heat and let the filling cool for 15 to 20 minutes.

9. Cut each puff pastry sheet into 4 rectangles, making 8 rectangles total.

10. Spoon the cooled beef filling onto one half of each pastry rectangle, leaving a border around the edges.

11. Brush the edges with beaten egg, fold the pastry over the filling, and press to seal.

12. Crimp the edges with a fork and cut a small slit in the top of each hand pie.

13. Brush the tops with the remaining beaten egg.

14. Bake for 18 to 22 minutes until puffed, crisp, and deeply golden.

15. Let the hand pies rest for 5 minutes before serving.