Preheat your oven to 400°F (200°C). This ensures that your pizza pockets will bake evenly and develop a nice golden color.
Roll out the pizza dough on a floured surface to about 1/4 inch thick. Use a pizza cutter or knife to cut the dough into squares, roughly 4x4 inches.
In a mixing bowl, combine the mozzarella cheese, pepperoni, bell peppers, olives, marinara sauce, Italian seasoning, salt, and pepper. Mix well until all ingredients are evenly distributed.
Place a generous tablespoon of the filling mixture in the center of each dough square. Be careful not to overfill, as this can make sealing the pockets difficult.
Fold the dough over to create a triangle and press the edges together firmly. Use a fork to crimp the edges, ensuring they are sealed completely.
Brush the tops of the pizza pockets with the beaten egg to give them a beautiful golden color as they bake.
Arrange the pockets on a baking sheet lined with parchment paper, leaving space between each one for even cooking.
Bake in the preheated oven for 15-20 minutes, or until they are golden brown and the cheese is melted inside. Keep a close eye on them towards the end of the baking time.
Once baked, remove the pizza pockets from the oven and let them cool for a few minutes. Serve warm with extra marinara sauce for dipping.