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Bring a medium saucepan of water to a boil over high heat.
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Cut the asparagus tips into 3-inch lengths then cut the remaining asparagus stalks into ¼-inch slices.
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Cook the asparagus in the boiling water for 30 seconds, or just until they become bright green.
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Drain the boiling water and transfer the asparagus to a large bowl of ice water until cool; drain the ice water.
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Preheat the broiler. Using a fork, whisk the eggs, salt, and pepper in a large bowl to blend well.
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Melt the butter in a 12-inch-diameter nonstick sauté pan over medium heat, swirling the pan to coat it with the butter.
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Add the eggs and asparagus, and gently stir with a silicone spatula to lift the cooked egg off the bottom of the skillet and stir it into the uncooked portion (be careful not to over stir the omelet).
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As the omelet begins to set, have one last gentle stir then scatter the cheese slices over the omelet.
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Place the pan under the broiler and cook for about 1 minute, or until the omelet is set on top and the cheese melts.
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Using the silicone spatula, loosen the omelet from the pan and slide it onto a platter. Cut the omelet into wedges and serve.