Prepare Eggnog Ice Cream (the day before): In a large bowl, whisk together the egg yolks and sugar aggressively until the mixture is thick and pale yellow in color. It should fall from the whisk in thick ribbons (otherwise known as ribbon stage). Combine the whole milk, heavy cream, and freshly grated nutmeg in a medium saucepan and bring to a rolling boil. Remove immediately from the heat. Temper the milk and cream mixture slowly into the egg yolk sugar mixture, whisking continuously.
Return the mixture to the saucepan and cook over low heat, stirring continuously, until the ice cream base has thickened and coats the back of a wooden spoon. Remove and pour the custard into a large bowl set over an ice bath. Stir in the brandy and allow the custard to cool completely, stirring every 5 or 10 minutes. Refrigerate the base overnight or until chilled. Freeze the ice cream according to your ice cream maker’s manufacturer’s directions. Just before the ice cream is finishing churning, add the chopped candied ginger. Line the bottom and sides of an 8-inch (20 cm) cake pan with wax paper. Spread the ice cream into the cake pan with an offset spatula until it is in a smooth flat layer. Cover with plastic wrap and foil, and allow to freeze for 4 to 6 hours or preferably overnight.
Prepare Gingerbread Cookies: Preheat the oven to 350°F (175°C) with a rack in the center position. Line a half sheet pan with parchment paper and set aside. In a medium bowl, whisk together the all-purpose flour, granulated sugar, ginger, cinnamon, baking soda, and salt. Add the molasses, oil, and half (beaten) egg and whisk to combine. Slowly pour in the boiling water and whisk until smooth. The batter will be thick.
Scoop the dough into balls (the dough should yield 12 cookies) and place onto the lined sheet pan, setting hte cookies at least 1-inch apart. Bake for 10 to 12 minutes. Transfer to a rack and allow the cookies to cool on the pan for 5 minutes, before transferring to a rack to cool completely.
Assemble the Ice Cream Sandwiches: Once the ice cream has chilled, remove from the freezer and lift the ice cream out of the cake pan. Using a 2½-inch biscuit cutter, cut the ice cream into six discs (the ice cream should be very firm, but not difficult to cut). For each ice cream sandwich, place 1 disc of ice cream between 2 gingerbread cookies. Gently press together (ice cream should spread to edge of cookies). Serve immediately or wrap well and freeze until ready to serve.