Step 1: Whip up the filling: In a medium saucepan, combine your diced peaches, both sugars, cornstarch, cinnamon, nutmeg, vanilla, and lemon juice. Pop it on your stove over medium heat. Stir until it starts to bubble and thicken, about 5–7 minutes. Once it looks like a nice, jammy consistency, take it off the heat and let it cool completely.
Step 2: Prep the dough: Preheat your oven to 375°F (190°C). Line a baking sheet with parchment paper. Unroll your pie crusts. Use a 4–6 inch round cutter, a bowl, clean can, or knife to cut shapes (circles, squares). You should get several shapes from each crust.
Step 3: Fill 'em up: Spoon a small amount of your completely cooled peach filling onto one half of each dough shape (circle or square). Fold the other half of the dough over the filling to create a half-moon or triangle shape. Use a fork to firmly press the edges all around to seal them tight. Brush the tops of your sealed hand pies with the beaten egg wash.
Step 4: Bake time! Carefully place your hand pies onto the prepared baking sheet. Slide them into your preheated oven and bake for 18–22 minutes until beautifully golden brown and slightly puffed. Take them out and let them cool slightly right on the baking sheet.
Step 5: Glaze 'em: While they're cooling a bit, whisk together the powdered sugar, milk (start with the smaller amount), and vanilla in a small bowl until it's smooth and pourable. If it's too thick, add just a tiny splash more milk until you get the consistency you like.
Step 6: Finishing touch: Once the hand pies aren't piping hot but still warm, either drizzle the glaze generously over the tops or carefully dip the top of each pie into the glaze. Let them sit for a few minutes so the glaze can set before serving.