Shaved ice–or “shave ice,” as it’s called in Hawaii–is thought to have originated in Japan in the 1860s, where it’s called kakigori. It came to Hawaii with Japanese plantation workers and quickly embedded itself in Hawaiian food culture. Today, it’s served over ice cream and topped with flavored syrups. For the fluffiest ice, use a shave-ice machine (about $35 from amazon.com). You can use a food processor to shave your ice, but it will be clumpier.
Make pineapple-mango syrup: Put pineapple cubes, mango slices, sugar, and 2 cups water in a medium saucepan and bring to a boil over high heat, stirring until sugar dissolves. Lower heat to a simmer and cook until pineapple and mango are softened, about 15 minutes. Let cool to room temperature, about 1 hour. Pour into a blender and purée into a thick syrup. Strain through a fine-mesh strainer and chill until ready to use.
Make plum syrup: Put plums, sugar, and 1 cup water in a medium saucepan. Bring to a boil over high heat, stirring until sugar dissolves, then lower heat to a simmer, cover, and cook 20 minutes. Let sit until slightly cooled, about 10 minutes. Pour into a blender with lemon juice and purée; taste and add more lemon juice if you like. Strain through a fine-mesh strainer, adding more water if needed for a thick syrup. Chill until ready to use.
Make shave ice: Process ice cubes in a food processor, 2 cups at a time, until cubes stop clattering and look like snow, with no lumps. Or, use a shave-ice machine.
Add a scoop of vanilla ice cream to each serving dish. Top with shave ice, then drizzle with either syrup plus a drizzle of sweetened condensed milk. Sprinkle with coconut flakes.
Make ahead: Syrups, chilled, up to 5 days. Shave ice, frozen, up to 1 day (whirl again before serving to break up icy clumps).
Per serving with 2 tbsp. Pineapple-Mango Syrup: 361 Cal., 14% (51 Cal.) from fat; 7.2g Protein; 5.6g Fat (3.6g sat.); 71g Carbo (1.6g fiber); 104mg Sodium; 28mg Chol.
Note: Nutritional analysis is per serving with 2 tbsp. Plum Syrup.
* Percent Daily Values are based on a 2,000 calorie diet. Your daily value may be higher or lower depending on your calorie needs.