Combine all ingredients in a food processor or blender. Cover and process or blend until nearly smooth. Press mixture through a fine-mesh strainer, one-third at a time, holding strainer over a bowl to catch juices (you should have about 1-2/3 cups strained juices). Discard solids. Transfer strained juice to a 2-quart square baking dish. Cover and freeze for 3 to 4 hours or until firm.

Break up frozen mixture. Transfer mixture to a chilled large bowl. Beat with an electric mixer until slushy, but not melted. Return to baking dish; cover and freeze for 2 to 3 hours or until firm.

To serve, scoop into small dessert dishes. If desired, top with cucumber pieces. Makes 8 servings.

Because jalapenos contain volatile oils that can burn your skin and eyes, avoid direct contact with chilies as much as possible. When working with chile peppers, wear plastic or rubber gloves. If your bare hands do touch the chile peppers, wash your hands well with soap and water.