Step 1

Bring sugar and water to a simmer in a small saucepan over medium heat; cook, stirring occasionally, until the sugar dissolves. Stir in lime zest and remove from heat. Cover and let steep for 1 hour, then strain the syrup through a fine-mesh sieve; discard the zest. (You'll have extra lime simple syrup; refrigerate for up to 1 week.)

Step 2

Add 1/2 cup of the simple syrup, lime juice, half-and-half and ice to a blender. Blend until the ice is crushed and the mixture is slushy. Divide among 4 8-ounce glasses and serve immediately.