In a small saucepan, combine 1/2 cup of the water, all of the sugar, and the finely grated zest of your lemons. Heat, stirring, until the sugar has completely dissolved, usually right before it begins to simmer. Add remaining 2 cups cold water and chill this mixture completely.

Set a fine mesh strainer over a large bowl (or a 4-cup measuring cup) and juice the lemons over it until you have 1 cup pulp-free juice. Chill this, too, until the syrup is cold.

Pour the chilled syrup through the strainer, removing the zest while adding it to the lemon juice.

Freeze mixture in an ice cream maker according to the manufacturer’s instructions.