Place thawed bread dough in a bowl in a warm area and let rise until doubled in size, 30 to 60 minutes.
Preheat oven to 350 degrees F (175 degrees C). Grease a baking sheet.
Spread dough into a large rectangle on the prepared baking sheet.
Mix 2 tablespoons Parmesan cheese, 2 tablespoons vegetable oil, egg yolks, parsley, oregano, garlic powder, and black pepper together in a bowl; spread mixture onto dough. Top Parmesan mixture layer with pepperoni, ham, and provolone cheese.
Heat 2 teaspoons vegetable oil in a skillet over medium heat; cook and stir green bell pepper, onion, and mushrooms in the hot oil until tender, 5 to 10 minutes. Spoon mixture over provolone layer.
Roll dough around the filling and place stromboli, seam side-down, onto the baking sheet. Brush the top of stromboli with egg whites; sprinkle 1 teaspoon Parmesan cheese and Italian seasoning over stromboli.
Bake in the preheated oven until dough is golden brown, 30 to 40 minutes.