Peppermint Snap Ice Cream Sandwiches

To make the ice cream, in a medium saucepan over medium heat, warm 2 cups of the half-and-half and the corn syrup until steam begins to rise from the surface, 3 to 4 minutes. Remove from the heat.

In a heatproof mixing bowl, whisk together the egg yolks, sugar and salt until blended. Form a kitchen towel into a ring and place the bowl on top to prevent it from moving. Gradually add the hot half-and-half mixture, whisking constantly until fully incorporated. Return the mixture to the saucepan and place over medium-low heat. Cook, stirring slowly and continuously with a wooden spoon or spatula, until the custard thickens and a finger drawn across the back of the spoon leaves a path, 8 to 10 minutes; do not allow the custard to boil.

Pour the custard through a fine-mesh sieve set over a clean bowl. Stir in the peppermint extract. Add the remaining 1 cup half-and-half and stir to combine. Nestle the bowl in a larger one filled halfway with ice and water and cool the custard to room temperature, stirring occasionally. Refrigerate until chilled, at least 1 hour.

Transfer the custard to an ice cream maker and freeze according to the manufacturer's instructions. At the end of the freezing stage, add the 1⁄2 cup peppermint candies and continue processing just until they are blended into the ice cream. Transfer the ice cream to a chilled container, cover and freeze until firm, 3 to 4 hours.

Spoon about 1⁄2 cup ice cream onto the center of a cookie, top with another cookie and gently squeeze together until the ice cream reaches the edges of the cookies. Using a slightly warmed butter knife, spread the ice cream flush with the edges of the cookies. Repeat to make 8 ice cream sandwiches. Freeze until firm, 2 to 3 hours.

Place the 1 cup peppermint candies in a shallow dish. Roll the outside edge of the frozen sandwiches in the peppermint snaps. Wrap the sandwiches with plastic wrap and freeze for at least 2 hours or up to 2 days before serving.