Preheat the broiler and position a rack 6 inches from the heat source. In a large nonstick, ovenproof skillet, heat 2 tablespoons of the olive oil. Add the chopped watercress, season with salt and black pepper and cook over high heat until wilted, 3 minutes. Drain the watercress well, then transfer to a bowl and let cool. Stir in the egg yolks and 1/4 cup of the cheese. Wipe out the skillet.
In a bowl, beat the egg whites with a pinch of salt until soft peaks form. Fold the whites into the egg yolks until no streaks remain.
Heat the remaining 2 tablespoons of olive oil in the skillet. Add the egg mixture, spreading it evenly. Cook over moderately high heat until the omelet is golden on the bottom, about 3 minutes. Sprinkle the remaining 3/4 cup of cheese on top and broil the omelet for 4 minutes, until the cheese is melted and the omelet is set on the top. Slide the omelet onto a platter, folding it in half. Cut the omelet into wedges and serve immediately.
Brisk, light white.
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