Bring the sugar, 1 cup water and ginger to a boil in a medium saucepan and cook until the sugar has melted. Transfer to a glass bowl or measuring cup, cover and refrigerate until cold, at least 2 hours and up to 24 hours.

Put the juice, zest, 1/4 cup ginger simple syrup, ginger liqueur and vodka in a blender and blend until combined. Taste for sweetness, adding more simple syrup if needed. Add a few cups of ice and blend until slushy, adding more ice as needed. Serve in a pitcher.