Preheat the oven to 400°F (204°C).
Toss the diced potatoes with 2 tablespoons of olive oil, salt, and pepper.
Spread them on a baking sheet and roast in the preheated oven for 20-25 minutes or until golden brown.
In a skillet over medium heat, sauté the chopped onion in 1 tablespoon of olive oil for 5-10 minutes until translucent.
Add the minced garlic and cook for about 30 seconds until just browned.
Add the ground beef to the skillet, season generously with Greek seasoning, and cook until the beef is thoroughly browned.
In a large bowl, mix the cooked beef, roasted potatoes, and optional crumbled feta.
Cut the pie crust into circles or squares. Place about 1/3 cup of the beef and potato mixture on each piece.
Fold the crust over the filling to create a half-moon shape, and use a fork to press and seal the edges.
Brush the top of each hand pie with the beaten egg for a golden finish.
Arrange the prepared hand pies on a baking sheet and bake at 400°F for 20-25 minutes, or until the pies are golden brown.
Enjoy the hand pies warm, served with tzatziki sauce on the side.