Heat 1 tablespoon of the oil in a large nonstick skillet over medium heat. Add the mushrooms and scallions and cook, stirring often, until tender, 2 to 3 minutes; remove from the skillet.
In a medium bowl, beat the egg whites with ¼ teaspoon each salt and pepper. Return the skillet to medium heat, heat the remaining tablespoon of oil, then cook the egg whites until they begin to set, 1 to 2 minutes.
Top with the vegetables and Cheddar. Fold the egg whites over the filling.
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