In a mixing bowl, combine the flour, salt, sugar, and instant yeast. Mix well to evenly distribute the dry ingredients.

Add the warm water and olive oil to the dry ingredients. Stir with a wooden spoon until a dough begins to form.

Knead the dough on a floured surface for about 5-7 minutes until smooth and elastic. This develops the gluten, which gives the dough its structure.

Place the dough in a lightly oiled bowl, cover with a clean kitchen towel, and let it rise in a warm place for about 30 minutes, or until doubled in size.

While the dough is rising, prepare the filling. In a bowl, combine the shredded mozzarella, pepperoni, bell pepper, and onion. Mix until evenly distributed.

Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper.

Once the dough has risen, punch it down to release the air. Divide the dough into 8 equal pieces.

On a floured surface, roll each piece into a circle about 6 inches in diameter.

Place a generous spoonful of the filling mixture on one half of each dough circle, leaving a small border around the edge.

Fold the other half of the dough over the filling to create a pocket. Press the edges together to seal, and crimp with a fork for a decorative touch.

In a small bowl, whisk together the beaten egg and water to create an egg wash. Brush the tops of the pizza pockets with the egg wash to give them a golden color when baked.

Place the pizza pockets on the prepared baking sheet and bake in the preheated oven for 15-20 minutes, or until golden brown.

Remove from the oven and let cool slightly before serving with pizza sauce for dipping.