Combine warm water, sugar, and yeast in a small bowl; let sit 5–10 minutes until foamy.
In a large bowl, mix flour and salt, then add the yeast mixture and olive oil. Knead on a floured surface 8–10 minutes until smooth, place in a greased bowl, cover, and let rise 1 hour until doubled. If the dough feels sticky, sprinkle in 1 tablespoon of flour at a time.
Mix mozzarella, provolone, and Parmesan with Italian seasoning and garlic powder. Slice pepperoni in halves for easier rolling. Warm the marinara slightly for easier spreading.
Preheat oven to 400°F (200°C) and line a baking sheet with parchment paper. Roll the dough into a 12×16-inch rectangle, spread a thin layer of marinara leaving a 1-inch border, then sprinkle the cheese mixture evenly and top with pepperoni.
Roll tightly from the long side into a log, tucking the ends in, and place seam side down on the sheet.
Brush the top with beaten egg, drizzle with olive oil, and sprinkle Parmesan, oregano, and coarse salt. Cut 3–4 shallow slits on top for steam to escape.
Bake 25–30 minutes until golden and crisp. Rest 5 minutes before slicing and serve with extra marinara.