Preheat the 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, roll each portion into a roughly 5-inch square. Transfer each square to the prepared baking sheet.

Spoon 1 tablespoon pizza sauce onto the center of each square, leaving about a 1/2-inch border around the edges.

Divide the 1 cup shredded mozzarella and the 1/2 cup sliced pepperoni evenly among the squares (about 2 tablespoons mozzarella and 1 tablespoon pepperoni per pocket). Spread the toppings over the sauce.

Fold each square in half over the filling to form a pocket. Gently press out any excess air, then firmly seal the edges by pressing with the tines of a fork.

Brush the tops and sealed edges of each pocket with the beaten egg.

Bake on the prepared sheet for 15 minutes, or until the pockets are golden brown. Let cool a few minutes before serving.