Activate the yeast by mixing it with warm water and sugar in a small bowl. Let it sit for about 5 minutes until it becomes frothy and bubbly, indicating it's ready.
In a large mixing bowl, combine the flour and salt. Pour in the activated yeast mixture and stir until a sticky dough begins to form.
Knead the dough on a floured surface for about 5 minutes until smooth and elastic. Cover with a damp towel and let it rest for 10 minutes to relax the gluten.
Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper.
Divide the rested dough into 8 equal pieces. Roll each piece into a flat circle about 4 inches in diameter.
Place a spoonful of pizza sauce, some shredded cheese, and a slice of pepperoni (if using) in the center of each dough circle.
Fold the dough over to enclose the fillings and pinch the edges together to seal completely, forming a tight pocket.
Brush the top of each sealed dough ball with the beaten egg for a golden finish.
Arrange the filled dough balls on the prepared baking sheet, leaving space around each for expansion.
Bake in the preheated oven for 15 minutes or until the outside is golden brown and crispy.
Remove from the oven, let cool slightly, and serve warm to enjoy the melty cheese and flavorful fillings inside the crispy crust.