In a mixing bowl, combine the sifted flour and salt. This helps to evenly distribute the salt throughout the flour.

Add the cold, cubed butter to the flour mixture. Use a pastry cutter or your fingers to work the butter into the flour until the mixture resembles coarse crumbs. This creates a flaky texture.

Gradually add the cold water, one tablespoon at a time, mixing until the dough comes together. You may need a bit more or less water depending on humidity.

Form the dough into a ball, wrap it in plastic wrap, and refrigerate for at least 30 minutes. Chilling the dough makes it easier to roll out.

In a skillet, heat the olive oil over medium heat. Add the diced onion and cook until translucent, about 3-4 minutes. This enhances the flavor of the filling.

Add the minced garlic and diced carrot to the skillet, cooking for an additional 2-3 minutes until the carrot softens.

Add the ground beef to the skillet, breaking it apart with a spatula. Cook until browned and no longer pink, about 5-7 minutes. Drain excess fat if necessary.

Stir in the oregano, thyme, salt, and pepper. Cook for another minute to allow the flavors to meld. Remove from heat and let cool slightly.

Preheat your oven to 400°F (200°C). Line a baking sheet with parchment paper.

On a floured surface, roll out the chilled dough to about 1/8 inch thick. Use a round cutter or a glass to cut out circles, about 5-6 inches in diameter.

Place a tablespoon of the beef filling in the center of each dough circle. Be careful not to overfill, as this can cause the pies to burst during baking.

Fold the dough over the filling to create a half-moon shape. Press the edges together to seal, then crimp with a fork for a decorative touch and to ensure they are sealed well.

Brush the tops of the hand pies with the beaten egg for a golden finish.

Place the hand pies on the prepared baking sheet and bake for 25-30 minutes, or until golden brown. This gives them a nice crispy texture.

Remove the hand pies from the oven and let them cool for a few minutes before serving. Enjoy them warm or at room temperature.