Gingerbread Cookie Ice Cream Sandwiches

Preheat an oven to 350 degrees F. Position a rack in the center of the oven. Grease a baking sheet or line with parchment paper, and set aside.

FOR THE COOKIES:
In a large bowl, beat together the butter, 1/3 cup granulated sugar, and brown sugar, using an electric mixer, until light and creamy. Beat in the molasses and egg until well blended. Sift the flour, baking soda, salt, ginger, cinnamon, and nutmeg into the molasses mixture, and beat until well blended.

With clean hands, form balls 1 1/2 inches in diameter (the size of large walnuts). Roll each ball in a bowl filled with the remaining 1/3 cup granulated sugar. Place the dough balls 4 inches apart on the prepared sheet. With the bottom of a custard cup or small bowl, flatten each ball into a 2-inch disk. Bake until the cookies are firm to the touch, about 12 minutes. Let the cookies cool slightly on the sheet before transferring to a wire rack to cool completely. Repeat with remaining dough. You should have about 32 cookies. Store or freeze the cookies in an airtight container at room temperature or in a freezer until ready to use.

FOR THE ICE CREAM:
In a saucepan, combine the half-and-half and sugar over medium-high heat and scald (bring almost a boil). Remove from the heat and let the half-and-half cool to nearly room temperature; otherwise, when the fresh ginger is added, the liquid may curdle. Stir in the grated ginger, cover, and allow to steep overnight in the refrigerator. Remove from the refrigerator and strain the liquid through a fine-mesh sieve. Discard the grated ginger.

In a large bowl, whisk the egg yolks until light yellow. Slowly whisk in the half-and-half. Pour the liquid into the top of a double boiler. Cook over water that has been brought to a boil and reduced to medium, stirring constantly with a wooden spoon, until the custard thickens and covers the back of the spoon, about 10 minutes. Strain the custard through a fine-mesh sieve into a container. Cover with plastic wrap and refrigerate until thoroughly chilled, at least 3 hours or as long as overnight.

Place the mixture in an ice-cream maker and freeze according to the manufacturer's instructions. Transfer the ice cream to a container, cover, and freeze for several hours.