To prepare the sorbet:
Combine the water, ginger, and sugar in a medium saucepan and bring to a boil over high heat. Remove from the heat and strain through a fine sieve with a puree press, discarding the ginger pulp.
Process the lychees and 1/2 cup of their syrup in a blender or food processor until smooth, about 2 minutes. Pour through a sieve set over the ginger water, again pressing with a puree press. Discard the pulp.
Freeze the lychee sauce in an ice cream freezer according to the manufacturer's directions. If you do not have an ice cream machine, freeze the liquid in a shallow baking pan until it is almost solid. This will take an hour or two depending on your freezer.
Once the sauce is frozen, remove it from the freezer and break into small pieces. Beat in the
large bowl of an electric mixer until smooth. Return the mixture to the shallow pan and refreeze. Repeat the freezing and beating process until you are satisfied with the consistency of the sorbet. The more times you beat, the smoother the texture will be, but it must be refrozen each time. One short beating will produce a granita. Several beatings will result in a richer, smoother texture.
When you are satisfied with the texture, transfer the sorbet to a covered storage container and let it ripen in the freezer for at least 30 minutes before serving.
To prepare the salsa:
This salsa should be made as close to serving time as possible in order to be at its best.
Toss the prepared mango, pineapple, mint, pepper, and strawberries in a small bowl and set aside until ready to serve. If you are using frozen strawberries, chop and add them at the last minute, still partially frozen, so they don't become limp.
To serve:
Place a scoop of the sorbet on a chilled dessert plate. Spoon 1/3 cup of the fruit salsa alongside and garnish with a crisp ginger cookie.
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