Wipe the mushrooms and thinly slice.
Thinly slice the mozzarella and cheddar.
Beat the egg whites until peaks start to form (you can do this manually with a wire whisk or, for convenience, with a hand or stand mixer).
Whisk the egg yolks with 1/4 teaspoon salt, all of the pepper and scallions.
Gently fold in the egg whites into the egg yolks.
Melt 1 tablespoon butter in a frying pan.
Saute the sliced mushrooms with the remaining salt for about a minute. Scoop out and transfer to a plate.
Melt the remaining butter in the pan. Pour in the eggs. Swirl the pan to allow the mixture to spread evenly. Coo over medium-low heat until the edges are firm but the top is still wet.
Spread the cheese slices on half of the omelet. Top with the sauteed mushrooms.
Fold the empty half of the omelet over to cover the cheeses and mushrooms. Continue cooking until the cheeses melt.
Slide the omelet onto a plate and serve immediately.