Bring water to boil in saucepan. Add ginger slices, cover and lower heat. Cook at low boil for 20 minutes. Strain. Put this strong ginger tea in blender jar with mint leaves and honey and blend well. Pour into ice cube trays and freeze.

Take the ginger-mint ice cubes and crush (with ice crusher or blender). Fill tall glasses with crushed ice. Pour sparkling mineral water over. Garnish with mint leaves.