Melt butter in a large nonstick skillet over medium-high heat. Stir in mushrooms, and cook until tender, about 5 minutes. Using a slotted spoon, transfer mushrooms to plate. Remove skillet from heat.
In a small bowl, beat egg yolks and milk to blend. In a separate bowl, beat egg whites with a dry beater until soft peaks form. Fold yolk mixture into whites.
Return skillet to medium-high heat. When butter sizzles, pour egg mixture into skillet. Sprinkle mushrooms and crab meat evenly over the top. Cook until omelet begins to set, about 3 minutes. Sprinkle with Swiss cheese. Using a large spatula, fold omelet over, forming semicircle. Cover skillet; cook until omelet puffs and is cooked through, about 3 minutes. Slide omelet onto large plate.
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