In a high-speed blender, combine all the ingredients for the sauce. Blend until smooth. Season with salt and black pepper to taste.
Heat up a nonstick pan or skillet over medium heat. Add 1 tablespoon olive oil.
Season the beaten eggs with salt and black pepper, then add to the heated pan. Use a spatula to soft scramble the eggs.
On a heated tortilla or lavash, layer with the soft scrambled eggs, grated mozzarella, sliced avocado, arugula or microgreens, and the verde sauce.
Fold up to seal the wrap and place in the same skillet you used to cook the eggs. Add more olive oil if needed to cook 1-2 minutes on each side, until golden brown and crispy. Enjoy warm!