Combine the water and ginger in a large pot. Bring to a boil and add the key lime zest. Turn the heat down to med-low and simmer for 10 minutes.

Remove from heat and strain the liquid through a fine wire mesh sieve into a medium bowl. Discard the solids.

Stir in the honey and place the bowl over a large bowl filled with ice and a little water.

Whisk occasionally while the mixture cools.

Once the mixture cools, add the key lime juice and process in an ice cream maker according to the manufacturers directions.

Put the mixture into the freezer in a freezer safe bowl and allow it to harden for about 2 hours.

The sorbet will have the consistency of a slushy when you scoop it out.