Finely dice mango to make 1 cup. Combine diced mango with ¼ cup sugar and 2 tablespoons vodka. Stir gently to combine, cover and chill in the refrigerator for a few hours.
Coarsely chop remaining mango and puree with an immersion blender. Strain puree and measure out 1¼ cups.
Whisk the xanthan gum with the remaining ¾ cup of sugar in a large mixing bowl. Whisk in the mango puree, lilikoi juice, half & half, and corn syrup, whisking until fully combined. Cover and chill in the refrigerator until very cold, about 2 hours. If you are short on time, freeze the mixture for about 15 minutes or until well chilled.
Process the mixture in your ice cream maker according to the manufacturer's instructions. My Cuisinart takes about 25 minutes. In the last minute of churning add the diced mangos (drain and discard liquid first ). Transfer ice cream to a covered container and freeze for at least 3 hours before serving.
Recipe by My Lilikoi Kitchen at https://www.mylilikoikitchen.com/2018/10/21/mango-lilikoi-ice-cream/