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In a small saucepan over medium-high heat, combine the salt, white pepper, Champagne, and 2 cups of the milk and bring just to a boil.
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Mix 2 cups of the hot milk mixture into the beaten egg yolks and whisk to blend. Mix this into the hot milk mixture remaining in the pan.
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Dissolve the cornstarch in the remaining 1/2 cup milk, add to the pan, and cook, whisking until the mixture thickens slightly, 6 to 8 minutes.
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Pour into a glass bowl, place a sheet of plastic wrap over the surface to prevent a skin from forming, and let cool. Refrigerate for 4 hours.
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To assemble, remove the Champagne cream from the refrigerator and whisk until smooth. Spoon 1 tablespoon of the chopped eggs into the bottom of a parfait or wine glass. Then layer 1 teaspoon of the chopped red onion, 1/2 teaspoon of the chopped parsley, 2 teaspoons of the caviar, 2 tablespoons of the Champagne cream, and 1 tablespoon of the salmon roe on top.
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Continue layering, using another 1 tablespoon chopped eggs, another 1 teaspoon red onion, 1/2 teaspoon parsley, and 2 tablespoons Champagne cream mixture, then another 1 tablespoon chopped eggs, 1 teaspoon chopped red onion, 1/2 teaspoon parsley.
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Top with 1 teaspoon of the caviar. Repeat the process to make 7 more parfaits. Cover and chill completely before serving.