Break the roasted chestnuts into smaller pieces, then purée them in a food processor until smooth. Tip: If it's too thick, add a little cream for easier blending.
Separate the egg yolks from the whites. You will need two yolks and one whole egg. In a heatproof bowl, whisk together the yolks, whole egg, honey, and vanilla extract.
Place the bowl over a simmering pot of water (double boiler), and whisk constantly until the mixture thickens (about 5-6 minutes). Be careful not to let it boil, or the eggs may curdle!
Let the egg cream cool, then add the chestnut purée and mix well. Set the mixture aside while you whip the cream.
In a clean bowl, whip the cold heavy cream until soft peaks form. Tip: The cream is ready when it forms soft peaks but isn't too stiff. This will ensure the parfait's lightness.
Gently fold the chestnut-egg mixture into the whipped cream. Be careful not to deflate the cream – use a spatula and stir in circular motions.
Pour the mixture into a silicone mold or a loaf pan lined with plastic wrap. Smooth the top and freeze for at least 6 hours, or preferably overnight.
Before serving, remove the parfait from the mold and let it sit at room temperature for 5-10 minutes to make it easier to slice. Garnish with extra chestnut pieces or sugar-free chocolate shavings, if desired.
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