In a medium bowl, combine the warm water, sugar, and yeast. Allow the mixture to sit for 5 minutes, once foamy and fragrant, add the oil, salt, and flour. Stir the mixture until a dough forms. Transfer the dough to a clean, greased bowl. Cover with plastic wrap and allow to rise for 1 hour or until doubled in size.
Meanwhile, in a large skillet over medium-high heat, warm the oil. Add the onion and cook until softened, about 5 minutes. Add the green pepper and cook until softened, about 3-5 minutes. Add the garlic, Italian seasoning, salt, pepper, and red pepper flakes; cook for 1 minute. Add the spinach, stirring until wilted, then add the tomatoes. Cook the mixture until slightly reduced, about 3-5 minutes, then remove from heat.
Once the dough has risen, transfer it to a floured surface and knead a few times. Roll the dough into a roughly 15x15-inch square and ¼-inch thick. Cut the dough down the middle to make 2 rectangles. Sprinkle each half with cheese and spread the spinach mixture on top. Starting from the long side, roll the dough up, tucking the ends under and pinching to seal the seams.
Brush the mixture with the egg and water mixture and top with sesame seeds. Use a sharp knife to score 4 vents into the tops of each stromboli.
Line the basket of the air fryer with parchment paper and place the stromboli, cooking one at a time, set the temperature to 350 degrees F, and cook for 15 minutes, until crispy and a light golden color. Slice and serve with marinara.