Combine the eggs, egg whites, Canadian bacon, water, green onion (if desired), and salt in a medium bowl.
Beat the mixture with a wire whisk or rotary beater until well mixed.
Lightly coat an unheated large nonstick skillet with cooking spray, and preheat over medium heat.
Add the egg mixture to the hot skillet, and cook, without stirring, until the mixture begins to set on the bottom and around the edge.
Using a spatula or a large spoon, lift the partially cooked eggs so the uncooked portion flows underneath. Continue cooking about 2 minutes or until the egg mixture is cooked through, but is still glossy and moist. Remove from heat immediately.
Fill the pita halves with the egg mixture, and sprinkle with cheddar cheese, if desired.