Mix the spices. In a small bowl, combine garlic powder, onion powder, smoked paprika, and dried oregano. Stir to blend and set aside.
Brown the beef. Heat a large pan over medium-high heat and spray with oil. Add ground beef, season with salt and pepper, and cook for about 5 minutes, stirring occasionally, until fully browned and no liquid remains.
Add pepperoni and spices. Add the chopped pepperoni and the spice mixture to the pan. Stir and cook for 2 more minutes until the pepperoni is lightly golden and fragrant.
Make the tomato filling. Add crushed tomatoes, tomato paste, and chopped parsley to the pan. Stir to combine, bring to a simmer, and cook for 2–3 minutes until the sauce thickens and reduces. Remove from heat. Allow the mixture to cool for a few minutes.
Assemble the rolls. Lay wraps flat. Divide the filling evenly among all 6 wraps, leaving a border around the edges. Top each with shredded mozzarella and a drizzle of your chosen sauce if using. Fold in the sides and roll up tightly like a burrito. Seal edges with a little water on your fingertips. Place seam-side down.
Toast until crispy. Place rolls seam-side down on a baking tray or air fryer basket. Lightly spray with oil. Bake at 400°F (200°C) for 8–10 minutes, or air fry at 350°F (180°C) for 8–10 minutes, until golden and crispy. Let cool a few minutes before slicing or serving.