In a large skillet over medium heat, brown one pound of ground beef, breaking it up with a spatula, for about 7-10 minutes until fully cooked. Drain any excess fat and stir in diced potatoes, carrots, celery, onions, and peas. Season generously with fresh thyme and simmer for 10-12 minutes until the vegetables soften and the mixture thickens. Set aside to cool.

Once the filling for your Savory Hand Pies is cooked, allow it to cool completely at room temperature for about 15-20 minutes. This step is crucial to avoid soggy pie dough.

Roll out the puff pastry on a lightly floured surface into squares, about 4-6 inches wide. Spoon a generous amount of the cooled beef and vegetable filling onto one half of each square. Brush the edges with egg wash and fold over to seal.

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

Place the assembled hand pies on the prepared baking sheet, brush the tops with egg wash, and bake for 24-26 minutes or until golden and flaky.

Let them cool on the baking sheet for about 5 minutes before serving warm.