Melt butter in a skillet over medium heat.
Use a vegetable peeler to thinly slice the potato into strips and place in an even layer in the pan (it is okay if there is a bit of overlap).
Cover with a lid and allow to cook, undisturbed, for 5 minutes.
Meanwhile, in a bowl, whisk together the egg and egg white.
Pour over the partially cooked potatoes.
Sprinkle with salt and pepper.
Cover and cook for 3-4 minutes until the egg is almost set.
Spread the cheese over half of the omelet, cover and cook for 2 more minutes until melted.
Remove from the heat and spread the avocado over the cheese followed by the tomatoes and green onions.
Fold over and remove to a plate.
