In a bowl, combine warm water, sugar, and yeast. Let it sit for 5 minutes until frothy.
Add olive oil, salt, and flour gradually, mixing until a dough forms.
Knead the dough on a floured surface for about 5 minutes until smooth.
Place the dough in a greased bowl, cover with a towel, and let it rise for 1 hour.
Preheat the oven to 375°F (190°C).
After rising, punch down the dough and roll it out into a rectangle.
Sprinkle shredded mozzarella and layer pepperoni evenly over the dough.
Roll the dough tightly from one end to the other and slice into 12 pieces.
Place the rolls in a greased baking dish and brush with egg wash.
Bake for 20 minutes or until golden brown. Let cool slightly before serving.