In a saucepan, combine sugar, ginger and 2 1/2 cups water. Cook over medium heat, stirring, until mixture begins to boil and sugar dissolves, 5 to 7 minutes. Remove from heat and let cool completely. Strain mixture through a fine-mesh sieve placed over a bowl, reserving syrup and discarding solids.
Place blueberries, lemon juice, salt and ginger syrup in a blender and blend until smooth.
Pour mixture into a 9-by-13-inch baking pan (preferably metal). Freeze for 4 hours, stirring every hour with a fork to scrape up and incorporate ice crystals. To serve, spoon into bowls and top with whipped cream and mint leaves, if desired.