Preheat the Oven: Begin by preheating your oven to 400°F (200°C). It’s important to get the oven nice and hot so you achieve that perfect flaky crust.
Cook the Vegetables: In a large skillet, heat the olive oil and butter over medium heat. Add the diced onion, carrot, and celery, sautéing until they are soft—about 5-7 minutes. Season with salt and black pepper to taste.
Add the Ground Beef: Stir in the pressed garlic and ground beef. Cook until the beef is browned, making sure to break it up with a spatula as it cooks. Drain excess fat.
Season and Thicken the Filling: Add the Italian seasoning, white pepper, tomato paste, and Worcestershire sauce. Sprinkle in the flour and stir to combine. Gradually add in the beef stock, bringing the mixture to a simmer. Allow it to thicken for about 5 minutes.
Mix in Remaining Ingredients: Stir in the diced potato, thyme, parsley, and green peas. Cook for an additional few minutes until the potato is tender. Remove from heat and let cool slightly.
Prepare the Pastry: On a floured surface, roll out the puff pastry sheets and cut them into circles. You can use a large cookie cutter or a bowl for this.
Fill the Pastry: Place a spoonful of the filling on one half of each pastry circle. Be careful not to overfill, or they may burst while baking!
Seal the Pies: Fold the pastry over to create a pocket and crimp the edges with a fork to seal. Place them on a baking sheet lined with parchment paper.
Egg Wash: Brush the tops of each hand pie with the whisked egg for a gorgeous golden finish. Dust with flaky salt, if desired.
Bake: Bake in the preheated oven for about 20-25 minutes, or until they are golden brown and puffed.
Cool and Serve: Allow the hand pies to cool slightly before serving. Enjoy warm!