In a skillet over medium heat, lightly toast the walnuts until fragrant and lightly golden brown.
In another bowl, whisk the egg yolks with the powdered sugar until you have a pale, frothy cream.
In a small saucepan over medium heat, heat the water. When it starts to boil, add the toasted walnuts and cook for 5-6 minutes, until the walnuts soften and the liquid thickens slightly.
Strain the walnut puree to remove any large pieces, then slowly pour the thick liquid into the egg yolk mixture, whisking constantly. Return the bowl to a double boiler and continue stirring until the mixture thickens slightly.
In a separate bowl, whip the heavy cream to stiff peaks. Make sure the cream is cold for easier whipping.
Gently fold the whipped cream into the egg yolk and walnut mixture. Use a spatula, being careful not to deflate the cream and maintain a light, airy texture.
Pour the mixture into a dish or a silicone mold, then place it in the freezer. Freeze for a minimum of 4-6 hours, but the flavors will meld even better if left to rest overnight.
5 minutes before serving, remove the parfait from the freezer to make it easier to slice. Dip a knife in warm water for clean cuts.
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