Combine the half & half, milk and sugar in a saucepan and gently warm until hot, but not boiling. Add the egg yolks to a separate large bowl and whisk until combined. Gradually pour in the hot milk and cream mixtures into the egg yolks, whisking constantly until combined.

Pour the mixture into a clean saucepan and heat over medium-low heat. Cook, stirring often, until the custard is thick enough to coat a wooden spoon and reaches a temperature of 170 degrees.

Pour the heavy cream and maple syrup into a separate large bowl and place a strainer over top. Strain the custard into the heavy cream and maple syrup. Add a pinch of salt, then stir together until well combined. Cover and chill for 4 to 6 hours, then freeze in an ice cream machine following the manufacturer's instructions. Freeze until ready to use.

To make the gingerbread cookies, whisk together the flour, spices, baking soda and salt in a mixing bowl.

In a separate large bowl, whisk together the brown sugar, melted butter, molasses and crystallized ginger. Add the egg and continue to whisk until blended.

Add the flour mixture and fold together using a rubber spatula until just combined.

Cover the bowl with plastic wrap and refrigerate for 1 hour or overnight.

Preheat oven to 350 degrees. Line a baking sheet with parchment paper or a silpat mat. Using a 1 tablespoon cookie scoop, roll the dough into a ball, flatten slightly and place 2 inches apart on the baking sheet. Bake until the cookies are puffy, about 11-12 minutes. Let the cookies cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.

When cookies have cooled, assemble ice cream sandwiches by adding a scoop of ice cream to the flat side of one cookie and then topping it with a second cookie.