For this gorgeous combination of green tea ice cream and ripe red plums poached in sweet sake, be sure to use fresh matcha (Japanese powdered green tea) and keep it tightly covered in the fridge--it oxidizes very quickly.
Stir ice cream and matcha together in a bowl. Freeze until firm, 3 to 4 hours.
Combine 1/2 cup sugar, the sake, ginger, and 1/3 cup water in a medium saucepan over medium-low heat. Cook, stirring, until sugar dissolves. Add plums and simmer over medium heat, covered, until fruit begins to soften, about 5 minutes.
Transfer plums with a slotted spoon to a bowl. Discard skins and ginger. Return liquid to stove; boil until reduced to 1/2 cup, 7 to 10 minutes. Pour over plums and chill until cool, about 20 minutes.
Whisk cream with remaining sugar in a bowl. Fold in candied ginger.
Spoon a third of plums and sesame snaps into 4 sundae glasses. Top with a scoop of ice cream. Repeat layering and top with remaining plums. Dollop with whipped cream and sprinkle with remaining sesame snaps.
*Find matcha at well-stocked grocery stores and at breakawaymatcha.com; find fruity nigori sake at liquor stores.