Lychees (often spelled 'litchis') are small, delicate fruits native to China and quite common in Hawaii. This recipe uses canned lyches as they're more readily available. The Fruit Salsa is just as delicious on frozen yogurt or low-fat ice cream.
Combine the first 3 ingredients in a medium saucepan; bring to a boil. Remove from heat; strain mixture through a double-layer cheesecloth-lined sieve into a bowl. Discard solids.
Strain lychees through a colander into a bowl, reserving 1/2 cup liquid; discard remaining liquid. Combine lychees and 1/2 cup liquid in a blender, and process until smooth. Strain mixture through a double-layer cheesecloth-lined sieve into bowl over ginger mixture. Discard lychee pulp.
Pour the lychee mixture and ginger syrup into the freezer can of an ice-cream freezer; freeze according to manufacturer's instructions. Spoon the sorbet into a freezer-safe container; cover and freeze 1 hour or until firm. Serve sorbet with Fruit Salsa. Garnish with mint sprigs, if desired.