In a saucepan, combine the butter, diced peaches, brown sugar, lemon juice, ground cinnamon, and cornstarch. Cook over medium heat, stirring occasionally, until the peaches release their juices and the mixture becomes slightly thickened (about 5-7 minutes). Remove the saucepan from heat and stir in the vanilla extract. Allow the filling to cool completely.

Preheat your oven to 375°F (190°C).

Lay out the thawed puff pastry sheet on a lightly floured surface. Using a round cutter, cut the puff pastry into even rectangles. You should get 6 rectangles from one sheet.

Place a spoonful of the cooled peach filling in the center of the rectangle leaving about 1/4" around each edge. Place another piece of pastry on top of each filled rectangle, creating a sandwich.

Use a fork to press and seal the edges of the hand pies. This will create a decorative crimped pattern and prevent the filling from leaking during baking.

Place the assembled hand pies on a parchment-lined baking sheet. Brush the tops of the hand pies with the egg wash, which will give them a golden, shiny finish during baking.

Bake in the preheated oven for 20-25 minutes, or until the hand pies are puffed up and golden brown.

Remove the baked hand pies from the oven and allow them to cool slightly before serving. Sprinkle with powdered sugar and enjoy!