In a bowl whisk together eggs, milk, salt, pepper., oregano, and parsley.
In a skillet add 1 teaspoon butter over medium-low heat. Once melted, add the egg mixture.Gently push in the sides of the eggs to help the uncooked egg to reach the heat.
Once the top of the eggs have set and are not liquidy add the gyro on one side. Follow with the onions, tomatoes, and cheeses. .
Allow cheese to melt for a minute.
Carefully, fold the omelette in half. Allow omelette to finish cooking for about 2-3 minutes. Top with tzatziki, onion, tomatoes, and feta cheese. Serve immediately.