In a small bowl, add eggs, milk, salt, pepper and stir.
In a medium sized bowl, combine chicken, mushrooms, green onion and parsley.
Put oil in an 8-inch skillet and add egg mixture. Cook on medium-low. As eggs set, run a spatula around the outside and lift, to allow uncooked portion of the egg to flow underneath. Cook eggs until almost set, but make sure that surface is still moist.
Press chicken mixture into top of egg mixture. Broil 4 to 5 inches from heat for 1 to 2 minutes.
Top off with cheese and broil until cheese is melted.