Preheat your oven to 375°F (190°C). Line two large baking sheets with parchment paper or silicone baking mats to ensure the pies do not stick and for easy cleanup later.
In a medium mixing bowl, combine the pumpkin puree, brown sugar, pumpkin pie spice, and vanilla extract. Stir until the mixture is smooth and the sugar has fully incorporated. Set this aside while you work on the crust.
Unroll the pie crusts onto a lightly floured surface. Using a pumpkin-shaped cookie cutter (about 3-4 inches wide), cut out 16 pumpkin shapes. You may need to gather the dough scraps and re-roll them to get all 16 shapes.
Take 8 of the pumpkin cutouts and use a small paring knife to carve out triangles for eyes and a mouth. These will be the “tops” of your hand pies. Leave the other 8 shapes solid; these will be the “bottoms.”
Place the 8 solid pumpkin shapes onto the prepared baking sheets. Spoon about 1 to 1.5 tablespoons of the pumpkin filling into the center of each shape, leaving a small border around the edges. Be careful not to overfill, as it might leak out during baking.
Lightly brush the edges of the bottom crusts with a little bit of water. Place the carved “face” crusts on top of the filling. Use a fork to crimp the edges firmly together, sealing the filling inside.
In a small bowl, whisk together the egg and 1 tablespoon of water. Lightly brush the top of each hand pie with the egg wash. This gives them a beautiful golden-brown finish. If desired, sprinkle with coarse sugar. Bake for 15 to 20 minutes, or until the pastry is golden and crisp.
Remove the pans from the oven and let the pies cool on the baking sheet for at least 5 to 10 minutes. This allows the filling to set so you don’t burn your mouth when taking that first delicious bite.