Saute mushrooms and onions in 1 tablespoon melted butter in a small skillet until tender; set aside.
Combine eggs, water, salt, and pepper in a medium bowl, beating with a wire whisk until blended.
Heat an 8-inch omelet pan or nonstick skillet over medium heat until hot enough to sizzle a drop of water. Add 1 tablespoon butter, and rotate pan to coat the bottom. Pour the egg mixture into the pan. As the mixture starts to cook, gently lift edges of omelet with a spatula, and tilt the pan so that the uncooked portion flows underneath.
Spoon the reserved mushroom mixture over half of the omelet in the pan, Loosen the omelet with a spatula, and fold the omelet in half. Carefully slide the omelet onto a serving plate. Garnish with a parsley sprig, if desired.