In a stand mixer fitted with the paddle attachment, cream the butter and 2/3 cup sugar together until light and fluffy, 2-3 minutes. Turn the speed down to medium-low and add the molasses, followed by the egg. Scrape down the sides of the bowl, all the way to the bottom.
Place a fine mesh strainer over the bowl and sift in the sweet white rice flour, mesquite flour, cornstarch, baking soda, cinnamon and ginger. Stir in the salt and crystalized ginger. Cover and chill the dough until firm, at least 1 hour. (Note: can be made up to 3 days in advance).
Preheat the oven to 325 degrees F and line 2-3 baking sheets with parchment paper. Place the remaining 1/2 cup sugar in a shallow bowl.
Scoop the dough into 1-inch diameter balls, roll in the sugar, and place on the prepared baking sheet 2-3 inches apart. Bake the sheets one at a time until the centers are soft and cracked and the edges are golden brown, 10-14 minutes. Allow to cool to room temperature. Store in an airtight container.
Prepare the ice cream:
In a medium, heavy-bottom saucepan, heat the milk, sugar, cinnamon, ginger, vanilla pod and seeds, and salt over medium heat until it begins to gently simmer. Remove from the heat, cover, and let steep for 30 minutes.
Once the mixture has steeped, place the egg yolks in a medium bowl. Reheat the milk until it’s steaming, then slowly whisk it into the egg yolks to prevent scrambling. Pour the mixture back into the saucepan and cook over low heat, stirring constantly with a heatproof spatula, until the mixture reaches 170 degrees F. Remove the saucepan from the heat, and whisk in the pumpkin puree, brown sugar and nutmeg.
Strain the mixture through a fine mesh strainer into a clean bowl and cover with plastic wrap, pressing it directly against the liquid to prevent a skin from forming. Chill until very cold, preferably overnight.
Prepare the ice cream in an ice cream maker according to the manufacturer instructions, then place in the freezer to continue firming up to a scoop-able consistency, approximately 2 hours.
To prepare the sandwiches, allow the ice cream to soften for several minutes. Place a small baking sheet in the freezer. Working swiftly, scoop approximately 1/4 cup of ice cream onto the flat side of one cookie, then top with a second cookie, gently pressing to flatten the ice cream slightly. Transfer to the baking sheet in the freezer, and continue preparing the remaining ice cream sandwiches. For long term storage, place the sandwiches in a large container or wrap individually for up to one month. For best results, let soften at room temperature for 5 minutes before serving.
Notes
Because ice cream bases are best chilled overnight before churning, and because you want the cookies to be completely cool before building the sandwiches, I recommend preparing this recipe over two days. Prepare the ice cream base and cookies on day one. Spin the ice cream and build the sandwiches on day two.Ingredients and instructions adapted slightly.Shared with permission from "Alternative Baker" by Alanna Taylor-Tobin