In a medium saucepan, bring the water to a boil over high heat, then add the honey and ginger and reduce the heat to medium. Simmer until reduced by half, about 30 minutes.
Remove from heat and add the mint, steeping for 10 minutes.
Strain the syrup into a measuring cup with a pour spout.
To serve, pour 1 tablespoon of syrup into an 8-ounce glass, fill with ice, then top with sparkling water.