Preheat your oven to 400°F. Prepare a baking sheet by lining it with parchment paper.
Heat a skillet over medium heat and lightly coat with cooking spray. Add the oil. Once heated, toss in the chopped spinach and sauté until wilted. Mix in the sun-dried tomatoes, garlic powder, Italian seasoning, salt, and pepper.
Shake the egg white carton well before pouring it over the spinach mixture. Stir a few times to ensure even distribution, then cover and cook until the eggs set into a patty.
Lay the lavash wrap flat. Place the cooked egg patty in the center and evenly distribute both mozzarella and feta cheeses over it.
Roll up the lavash wrap like a burrito, ensuring the bottom is sealed. Lightly spray both sides of the wrap with cooking spray and place it on the prepared baking sheet.
Bake in the preheated oven for 5-8 minutes, flipping halfway through, until it reaches your desired level of crispiness. Once done, slice the wrap in half and enjoy your homemade Starbucks-style spinach feta wrap!