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1
Preheat the oven to 375F.
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2
In a 10-inch non-stick skillet simmer the asparagus in water to cover for 3 to 5 minutes, or until it is just tender.
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3
Drain the asparagus, rinse it under cold water, and pat it dry with paper towels.
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4
Cut the asparagus crosswise into 1/4-inch pieces and transfer the pieces to a bowl.
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5
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.
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6
Add the sugar, cook the mixture, stirring, for 3 to 5 minutes, or until the onion is golden, and transfer the mixture to the bowl.
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7
Stir in the Gruyere, the tarragon, and salt and pepper to taste.
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8
In the skillet, cleaned, heat the remaining 1/2 tablespoon butter over moderate heat until it is melted, tilt the skillet to coat it, and remove it from the heat.
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9
In a bowl whisk the egg yolks with the flour and salt and pepper to taste until the mixture is thick and lemon-colored.
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10
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.
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11
(If the skillet handle is plastic, wrap it in a double thickness of foil.)
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12
Bake the omelet in the middle of the oven for 7 minutes, or until it is puffed and almost cooked through, spoon the filling down the middle of it, and with a spatula fold the omelet in half to enclose the filling.
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13
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.
