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In a 9-inch (23 cm) non-stick skillet over low heat, soften the leek slices in the oil, covered, for about 4 minutes on each side. Evenly space out the leek slices in the skillet.
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Gently pour the eggs into the skillet, without moving the leek slices. Sprinkle with the cheese. Season with salt and pepper. Continue cooking for 5 minutes, covered, without touching.
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Slide the omelet flat onto a plate.
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Serve with a slice of country bread and a green salad, if desired.
NOTE
For this recipe, you can use the white and light green parts of the leek. Goat cheese can be replaced with diced Oka cheese, with or without the rind.