Cut the eggplants into wedge-shaped sections of the size of the leaves desired. Slice away the seeds.
Cut curving openings in the skin of the eggplant to give the appearance of the veins of a leaf. Work from the base to the tip of the leaf.
Cut notches in the two outer edges of the leaf, aligning them attractively with the veins and making the cuts deep enough that the notches are well defined. When finished, soak the leaf in a mixture of water and lime juice to prevent it from blackening.
Slice cucumber lengthwise into thirds. Use the two outer portions, which have the fewest seeds.
Place one portion on a cutting board peel side up. Take a diagonal slice toward one end and discard the end. Then, cut five thin slices so that they remain attached at one end. Cut the five slices from the cucumber, and then continue slicing the cucumber in the same way.
Fold the tips of the free ends of the first, the third, and the fifth slice over and tuck them into the attached end.
Cut the cucumber lengthwise into fairly thick slices. Cut the slices diagonally to obtain pieces shaped like a rhombus.
Trim each piece to shape it like a leaf.
On the green side, cut a groove to represent the midrib, and then cut diagonal grooves to represent the veins. These should be spaced to give an attractive alternating green and white pattern. Finally, cut notches around the edges of the leaf.
Cut off the stem end of the cucumber to obtain a flat, stable base.
Form the handle of the basket by making two parallel cuts about 3 mm. apart extending from the tip down about two thirds of the length of the cucumber and then cutting off the excess on either side.
Carefully remove the flesh from within the handle and hollow out the body of the basket.
Cut closely spaced notches around the mouth of the basket.
Cut a shallow, narrow groove around the outside of the basket just below the edge.