Beat eggs and milk lightly. Add cheese, onion, parsley, salt and pepper.
Heat oil in a heavy skillet. Pour in egg mixture and reduce heat as edges of omelet begin to thicken.
With a fork, draw cooked portions toward center to allow uncooked mixture to flow to bottom of skillet. Shake and tilt skillet as necessary to aid flow of uncooked eggs. Do not stir. When eggs no longer flow and surface is still moist, increase heat to quickly brown the bottom of omelet. Loosen edges carefully and fold omelet over.