Chestnut Ice Cream with Chocolate Grand Marnier Sauce

Finely chop chestnuts and cook with 1 1/4 cups milk at a bare simmer in a large heavy saucepan, uncovered, stirring occasionally, 15 minutes. Purée in a blender until smooth (use caution when blending hot liquids). Bring cream and remaining 1 3/4cups milk just to a simmer in heavy saucepan and remove from heat. Beat together yolks and brown sugar in a large bowl with an electric mixer at high speed until thick and pale and mixture forms a ribbon when beaters are lifted. Whisk 1/3 of hot cream mixture into yolk mixture to temper, then whisk yolk mixture into remaining cream mixture. 3Whisk in chestnut purée and salt, then add zest. Cook over moderately low heat, stirring constantly, just until mixture registers 170 °F on an instant-read thermometer (do not boil). Immediately pour custard through a fine sieve into a clean metal bowl and stir in vanilla. Set bowl in a larger bowl of ice and cold water and cool custard, stirring occasionally. Chill, surface covered with waxed paper, until cold, at least 3 hours. Freeze custard in ice-cream maker, then transfer to an airtight container and put in freezer to harden.