1 tablespoon minced fresh tarragon leaves, or to taste
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Let's Make It
Preheat the oven to 375 degrees F. In a 10-inch non-stick skillet simmer the asparagus in salted water to cover for 3 to 5 minutes, or until it is just tender. Drain the asparagus, shock in ice water, and pat dry with paper towels.
In the skillet, cook the onion with salt and pepper, to taste, in 1 tablespoon of the butter over moderate heat, stirring frequently, for 5 minutes, or until the onion is golden, and transfer the mixture to the bowl. In the same skillet, heat asparagus until warmed through. Add the asparagus to the onions.
Wipe out the same skillet and heat the remaining 1/2 tablespoon butter over moderate heat until it is melted, tilting the skillet to coat it with the butter, and remove it from the heat.
In a bowl, whisk the egg yolks with the flour and salt and pepper, to taste, until the mixture is thick and lemon-colored. Add the onions and asparagus to the egg yolks.
In another bowl with an electric mixer, beat the egg whites with a pinch of salt until they just hold stiff peaks, fold them into the yolk mixture gently but thoroughly, and pour the egg mixture into the skillet, spreading it evenly. (If the skillet handle is plastic, wrap it in a double thickness of foil.)
Bake the omelet in the middle of the oven for 7 minutes, or until it is puffed and almost cooked through. Spoon the Gruyere and tarragon, and a dash of salt and pepper down the middle of the omelet, and with a spatula fold the omelet in half to enclose the filling. Bake the omelet in the middle of the oven for 1 minute more, or until the cheese is melted and the omelet is cooked through.