Preheat oven to 400°F (200°C). Line a baking sheet with parchment paper.
Divide the 1 pound refrigerated pizza dough into 8 equal portions.
On a clean work surface or on the prepared parchment, roll each portion into a 5-inch square. Place the squares on the prepared baking sheet, leaving space between them.
Spoon 1 tablespoon of pizza sauce onto the center of each square, leaving a 1/2-inch border around the edges.
Evenly divide the 1 cup shredded mozzarella cheese among the squares, sprinkling the cheese over the sauce on each one.
Evenly divide the 1/2 cup sliced pepperoni among the squares and place the slices on top of the cheese.
Fold each square in half over the filling to form a pocket. Press the edges together to seal, then crimp the sealed edges with a fork to ensure they are closed.
Brush the tops and edges of each sealed pocket with the beaten large egg.
Bake on the prepared baking sheet for 15 minutes, or until the pockets are puffed and golden brown.
Remove from the oven and let the hot pockets cool on the baking sheet for about 5 minutes before serving.