1. In a food processor, combine the flour and salt. Add the chilled butter and pulse until the mixture resembles coarse crumbs. Slowly add the ice water and pulse until the dough just begins to come together.

2. Turn the dough out onto a lightly floured surface and gently shape into a disc. Wrap in plastic wrap and refrigerate for at least 1 hour.

3. In a large skillet, cook the ground beef over medium-high heat until browned and crumbled, 5-7 minutes. Drain any excess fat.

4. Add the onions, carrots, celery, and garlic to the skillet. Cook, stirring occasionally, until the vegetables are softened, about 8-10 minutes.

5. Stir in the thyme, rosemary, beef broth, Worcestershire sauce, and tomato paste. Simmer for 15-20 minutes, until the filling has thickened. Season with salt and pepper to taste.

6. Preheat your oven to 400°F (200°C).

7. On a lightly floured surface, roll out the chilled dough to 1/4-inch thickness. Cut out 6 rounds using a 5-inch circular cookie cutter or biscuit cutter.

8. Place the dough rounds into a 6-cup muffin tin, pressing the dough into the cups and up the sides to form the pie shells.

9. Spoon the beef filling evenly into the prepared pie shells.

10. Roll out the remaining dough and cut out 6 smaller rounds to use as the pie tops. Place the top rounds over the filling and crimp the edges to seal.

11. Brush the top of the pies with a beaten egg or milk.

12. Bake for 25-30 minutes, until the crust is golden brown.

13. Allow the pies to cool for 5 minutes before serving.