Combine the water and sugar in a small pot and bring to a boil until all the sugar dissolves. Stir in the lemon juice and zest. Remove from the heat and carefully pour the mixture into a medium bowl. Chill in the refrigerator until cool.
Transfer the bowl to a freezer and freeze the mixture for about 3-4 hours. Remove the bowl from the freezer, mix the mixture with a fork and return the bowl to the freezer. Repeat this process a few times for an additional 2 hours.
When the ice is ready to be served, scoop into individual bowls and sprinkle the peppermint over the top. Serve immediately.