Step 1Dice the cucumbers into 1-inch pieces; do not peel the skins. Place the pieces in a food processor and puree until smooth. Strain into a medium bowl through a fine mesh strainer, pushing the juice out with some of the pulp. You should have 2 1/2 cups of juice and pulp. Set aside.
Step 2To a small saucepan, add the lime juice and sugar. Crush the dried peppers in your hands and add to the saucepan. Cook over medium heat, stirring occasionally, until the sugar is dissolved. Remove the syrup from the heat and cool slightly.
Step 3Strain the cooled syrup into the bowl with the cucumber juice and pulp, discarding the crushed peppers. Stir in the salt. This makes about 3 cups base.
Step 4Place the granita base in a large baking dish. Freeze, stirring every half-hour or so until the granita is frozen. To serve, shave the granita, raking the tines of a fork across the surface to break up the crystals. Serve immediately.