In a skillet, heat avocado oil over medium-low until hot.
While the oil is heating up, slice mushrooms and green onion. Put aside. In a small bowl add the egg and egg whites and whisk together.
Add the sliced mushrooms to the pan and sauté until tender. Then add the egg mix, the green onion, salt and pepper, and vegan cheese and mix occasionally until eggs are cooked through. You want to make a scrambled egg-veggie mix.
Lay a tortilla wrap flat and add the egg mixture to the centre of the tortilla. Wrap it like a burrito by folding the bottom end up over the egg, tightly. Then tuck in the corners and roll over until the burrito is sealed.
Keeping the pan on med-high, add the burrito sealed side down onto the pan and cook until slightly browned. Flip and cook until the other side is slightly browned.
If you're eating immediately, serve with a side of salsa, vegan sour cream if you'd like. If you're going to freeze the burrito, wait until it's cooled before wrapping in wax paper.