Using a large mixing bowl, combine ½ cup of flour with the yeast, sugar and water. Stir until well combined; let mixture rest for 15 minutes.
Add the remaining flour, olive oil and salt; mix on low speed until well combined. Increase speed to medium and mix for 3-4 minutes. Transfer dough into a lightly oiled bowl, cover and let rest at room temperature for 1 hour.
Turn dough out onto lightly floured countertop and fold several times. Place back into bowl, cover and let rest at room temperature for ~30 minutes, or until dough has doubled in size.
For the Filling
Lightly dust countertop with flour. Roll dough into an 11”x17” rectangle. (Note: You could also make two smaller strombolis, but we opted for one long one instead.)
With a long side of the dough facing you, spread the pizza sauce (if using) evenly across dough, leaving 1” border on both of the longer sides. Next, spread the mozzarella evenly across dough. Sprinkle 1 tsp of Italian seasonings on top of cheese.
Overlapping slightly, layer the ham, salami, pepperoni and provolone lengthwise down the dough. Sprinkle Parmesan cheese evenly on top.
Brush the long edge of the dough closest to you with the beaten egg. Starting with the opposite long end (the one without the egg wash) roll the dough towards you into a tight cylinder. Pinch edges of dough to seal.
Brush top of dough with remaining egg wash and sprinkle with remaining ¼ tsp of Italian seasonings and kosher salt.
Preheat oven to 400°F. While oven heats, let Stromboli rest at room temperature for ~15 minutes.
Cut 3 (½”) steam vents in top of Stromboli. Bake at 400°F for 20-25 minutes, or until top of Stromboli is golden brown. (Note: If you have a pizza stone, place it into the oven while it preheats and then bake directly on the stone. If not, then bake this Stromboli on the bottom rack of the oven using a standard baking sheet.)