Thinly slice mushrooms and green onions. Dice sliced ham. Saute in pan with 1 tablespoon butter for approximately 3-5 minutes. While these saute, wisk eggs in bowl. Add milk, salt, and pepper blending together.
Heat a nonstick 8" omelet pan over medium-high heat melting remaining 1 tablespoon butter while tilting pan to coat entire surface.
Pour eggs into pan and cook until they just begin to set. Begin to scramble eggs using a heat proof rubber spatula. When eggs form soft, moist curds, spread them into an even layer. Sprinkle the Gruyere evenly down the center of omelet. Immediately add mushroom, onion, and ham mixture onto the cheese along the same line. Continue to cook without stirring the omelet for another minute until the omelet is set.
Place the edge of the omelet pan on a work surface next to the serving plate. Tilt the pan to one side slightly while using rubber spatula to lift the higher side and fold it over to form a half circle shape. Use spatula to slide omelet onto serving plate. Lightly brush the top of the omelet with any residual butter from the mushroom, onion and ham pan to give the omelet a slight sheen. Sprinkle lightly with chopped Italian parsley.
Serve with fruit garni and favorite whole grain breads.