Step 1Chill a shallow baking dish in the freezer.
Step 2In a blender, puree the melon and currants with 1 cup sugar. Add the lemon juice and blend once again. Taste and add more sugar if necessary (the mixture should be a little sweeter than you might think, because it will be less sweet after being frozen).
Step 3Strain the melon mixture through a sieve to extract the juice and pulp. Pour into the baking dish and freeze, about 30 minutes.
Step 4When the melon mixture stars to set, mix it with a fork to break up the ice crystals and return it to the freezer. Repeat these steps every 30 minutes until the mixture has set and has a smooth, slightly grainy texture. This will take about 2 hours.
Step 5Serve in glass bowls, garnished with sprigs of mint.