Step 1Peel two of the cucumbers but leave the peel on the third cucumber for color. Rinse the cucumbers to remove any residue or dirt.
Step 2Trim the ends off the cucumbers and slice them in half lengthwise. Scoop out the seeds. Cut the cucumbers into 2-inch chunks and puree them in a blender or food processor along with one-fourth cup water. Add the lime juice, sugar, pepper and salt.
Step 3Pour the mixture into an ice cream maker, and freeze according to manufacturer's instructions.
Step 4Spoon the granita into a chilled glass dish until it is firm enough to hold its shape. Serve a small scoop in a bowl as a palate refresher between courses.