Prepare the Dough. Combine warm water, sugar, and active dry yeast. Let it sit for 5 minutes until the yeast becomes frothy. In a separate bowl, mix the flour and salt. Create a well in the center and pour in the yeast mixture and olive oil. Stir until a shaggy dough forms. Transfer the dough to a floured surface and knead for 5-7 minutes until it becomes smooth. Place the dough in a greased bowl, cover it with a kitchen towel, and let it rise for 1-2 hours or until doubled in size.
Assemble the Filling. While the dough is rising, slice the deli meats, provolone cheese, bell peppers, onions, mushrooms, and black olives. Preheat the oven to 400F.
Roll Out the Dough. Once the dough has risen, transfer it to a floured surface and punch it down to release the air. Roll the dough into a rectangular shape, approximately ¼ inch thick.
Fill and Roll. Spread the marinara sauce evenly over the dough, leaving a small border around the edges. Layer the meats, provolone, bell peppers, onions, mushrooms, and black olives on top of the sauce. Sprinkle on the Italian herbs, salt, and pepper. Starting from one of the longer edges, roll the dough into a log, sealing the ends tightly.
Bake the Stromboli. Transfer the Stromboli onto a baking sheet with parchment paper. Brush the top with the egg wash for a glossy, golden crust. Add small slits on top to allow steam to escape during baking. Place the baking sheet in the oven and bake for 25-30 minutes until the Stromboli is golden brown.
Serve and Enjoy! Remove the Stromboli from the oven and let it cool. Slice it into thick pieces and serve it warm.