Cook the rice in the carrot juice and vegetable broth mixture according to the package instructions over low heat without a lid for about 20 to 25 minutes. The liquid should be completely absorbed or evaporated. Stir in the grated cheese, season with salt if necessary. Let the mixture cool down a little.
Shape the rice into balls with moistened hands. Cut the eyes and mouth from the olives, the stalk from the thickly sliced cucumber peel. Press the pieces lightly into the rice balls.