Preheat the broiler and position a rack in the center of the oven. In a large bowl, using a whisk or a handheld electric mixer, beat the egg whites until soft peaks form.
In a small bowl, whisk the egg yolks with the salt and one-fourth of the beaten egg whites. Fold the yolk mixture into the remaining beaten whites until no streaks remain.
In an 8-inch ovenproof skillet, melt the butter. Scrape the omelet mixture into the skillet and shake gently to evenly distribute the eggs. Sprinkle the cheese all over and transfer the skillet to the oven. Broil the omelet for about 3 minutes, until lightly browned and very puffy. Carefully slide the omelet onto a plate, folding it in half. Serve right away.