1. In a bowl, combine 3/4 cup of the sugar, cream, milk and cornstarch to create an ice cream base. In a spice grinder, mix the whole spices and grind for a half a minute or so. (A coffee grinder will work just fine.) Transfer the spice mixture to a heavy pan (cast iron works well), add the ginger, and cook over low heat for a minute or two until the mixture becomes fragrant.
2. Stir the spice mixture into the ice cream base. Pour the mixture into your ice cream maker and freeze according to the manufacturer's instructions.
3. Combine the salt and the remaining cup of sugar in a bowl. Once the ice cream is ready, you will have to work quickly. Scoop one scoop of ice cream and, using tongs, place it in a container filled with the dry ice for approximately 20 seconds. Then transfer it to the sugar mixture and coat well. Repeat the process until you have six to eight scoops ready.
4. The grill should be at medium-high heat. Because of the dry-ice treatment, the ice cream is at a temperature well below freezing. The idea is for the intense heat of the grill to rapidly caramelize the sugar and milk solids into an exterior crust, before the heat penetrates to the cold interior. It may take one or two scoops before you get the timing right. Work with one scoop at a time, using tongs to ensure an even browning of the exterior.
5. Transfer the scoops to serving dishes, garnish with a few shavings of lemon zest, or whatever else suits your fancy. Enjoy!
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