Preheat oven to 425°F. Line a large baking sheet with parchment paper.

Add the diced Granny Smith and Dazzle apples, butter, brown sugar, cinnamon, salt, and lemon juice to a medium skillet.

Cook over medium heat for 5–7 minutes, stirring often, until the apples begin to soften and release their juices.

In a small bowl, stir together the cornstarch and water until smooth. Pour into the apple mixture and cook for another 1–2 minutes, stirring constantly, until the filling becomes thick, glossy, and sticky.

Remove from heat and stir in the vanilla. Transfer the filling to a bowl and allow it to cool for about 10 minutes.

Unfold the thawed puff pastry sheets on a lightly floured surface. Gently roll each sheet just enough to smooth the seams.

Cut each sheet into 8 equal rectangles, for a total of 16 rectangles.

Spoon about 1½ tablespoons apple filling into the center of 8 pastry rectangles, leaving about a ½-inch border around the edges.

Place the remaining pastry rectangles over the filling. Press the edges together, then seal firmly with the tines of a fork.

Transfer the hand pies to the prepared baking sheet. Use a sharp knife to cut 2–3 small slits in the top of each pie.

Refrigerate the assembled hand pies for 10–15 minutes.

Whisk together the egg and 1 tablespoon water. Brush the tops of the chilled hand pies lightly with the egg wash.

Very lightly brush the tops with the melted butter.

Stir together the granulated sugar and cinnamon. Sprinkle generously over each hand pie.

Bake at 425°F for 5 minutes.

Without opening the oven, reduce the temperature to 400°F and continue baking for 9–12 minutes, or until the hand pies are puffed, blistered, and deeply golden brown.

Allow the hand pies to cool on the baking sheet for about 5 minutes, then transfer to a wire rack. Serve warm or at room temperature.